Showing 1–41 of 41 results for all: equality saturation vectorization

The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon

Authors: Alexander Temerev, Alessio Doria

Abstract: …, the isosceles triangle with equal sides $1$ and apex angle $108^\circ$: the shortest curve guaranteed to reach the boundary of $G$ from an unknown starting position and heading is a symmetric seven-piece path of segments, circular shoulders, and tangents, of exactly determined length $C=1.282676025459\ldots$. To our knowledge, this is the first proved exac… ▽ More We solve Bellman's lost-in-a-forest problem for the golden gnomon $G$, the isosceles triangle with equal sides $1$ and apex angle $108^\circ$: the shortest curve guaranteed to reach the boundary of $G$ from an unknown starting position and heading is a symmetric seven-piece path of segments, circular shoulders, and tangents, of exactly determined length $C=1.282676025459\ldots$. To our knowledge, this is the first proved exact optimum for an isosceles triangle whose base angle is below $45^\circ$. The curve's parameters come from one isolated quartic root, and $C$ is transcendental. Equivalently, $C^{-1}G$ is the smallest homothetic golden-gnomon cover of all unit arcs. The proof introduces a balanced support calibration: one weighted family of escape inequalities, built on the linear relation among the triangle's three normals, exactly saturated by the candidate, through eighteen exact support windows, and confronting every shorter competitor at once. Aggregation along the normal fan compresses the calibration to a finite zero-sum family of supported vectors; summation by parts then bounds its total by path length whenever the running suffix balance, the ledger, stays in the unit disk. A local two-gap surgery and cyclic bitonicity force a shortest hypothetical counterexample into exactly the temporal order the ledger tolerates. Lean 4 verifies the two finite algebraic certificate families and the reusable discrete ledger identities and bounds. △ Less

Submitted 27 July, 2026; originally announced July 2026.

Comments: 27 pages, 3 figures. Lean 4 formalization and independent audits are included as ancillary files and maintained at https://github.com/atemerev/gnomon

MSC Class: 52A40 (Primary); 52C15; 49Q10 (Secondary)

Demixing Sparse Signals from Nonlinear Observations using Generalized Non-convex Regularization

Authors: Raziyeh Takbiri

Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated. We propose a regularization… ▽ More We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated. We propose a regularization-based framework combining a Huberized data fidelity with generalized folded-concave penalties (SCAD, MCP), and a two-block proximal alternating algorithm with backtracking (NLD-PALM) whose whole iterate sequence provably converges to critical points under the Kurdyka--Łojasiewicz property, with local linear rates. On the statistical side we establish restricted strong convexity of the Huberized nonlinear loss through an exact sign-definite decomposition, and derive estimation error bounds of order $σ\sqrt{s\log(n)/m}$ that hold at \emph{every} localized stationary point, an oracle rate $σ\sqrt{s/m}$ free of $\log n$ and shrinkage bias under a beta-min condition, and a co-equal recovery theorem for \emph{unknown} monotone links via a linear surrogate and a clipped Plan--Vershynin decoupling. The estimator requires no knowledge of the sparsity levels, and its guarantees hold under symmetric noise with only finite variance. Experiments at $n=512$ under a frozen data-driven regularization rule show an earlier phase transition than convex $\ell_1$ demixing and greedy hard-thresholding baselines, a $35\times$ accuracy advantage over squared-loss estimation under $5\%$ gross outliers, and successful demixing of spike-plus-background signals observed through a saturating amplifier. △ Less

Submitted 12 July, 2026; originally announced July 2026.

Equality Conditions for an Additive Three-Observable Uncertainty Relation

Authors: Yao-Yi Zeng, Zhi-Jie Liu, Jie Zhou, Jing-Ling Chen

Abstract: …a short rotational derivation by rotating the observable triple and applying the Robertson uncertainty relation to the two transverse observables. This derivation makes the saturation mechanism transparent and leads to a necessary and sufficient condition for… ▽ More Uncertainty relations play a fundamental role in quantum mechanics by quantifying the intrinsic limitations on the simultaneous sharpness of incompatible observables. Beyond the standard two-observable product form, additive uncertainty relations for triples of observables provide a natural framework for describing collective constraints among three noncommuting components. In this work, we study an additive uncertainty relation for three Hermitian observables from the viewpoint of rotational symmetry and covariance geometry. We give a short rotational derivation by rotating the observable triple and applying the Robertson uncertainty relation to the two transverse observables. This derivation makes the saturation mechanism transparent and leads to a necessary and sufficient condition for equality for general density operators. In the nontrivial equality case, the covariance ellipsoid of the observable triple degenerates into a disk perpendicular to the expectation value of the commutator vector. We also discuss an inverse construction based on finite-dimensional representations of the Lie algebra \(\mathfrak{su}(2)\), which provides a systematic way to construct observable triples with prescribed saturating states. These results clarify the geometric and representation-theoretic structure underlying the tightness of additive three-observable uncertainty relations. △ Less

Submitted 29 June, 2026; originally announced June 2026.

Comments: 8 pages, 1 figure

Squeezing-enhanced Pairwise Fusion of Photonic Qudits

Authors: Pradip Laha, Peter van Loock

Abstract: …to definite pairwise Bell projectors. We derive the exact logical-space POVM and prove that a diagonal pattern is accepted if and only if its photon-number-imbalance vector has exactly two nonzero components of… ▽ More Pairwise fusion gates are linear-optical measurements that herald Bell projections onto two-rail subspaces of two \(d\)-rail single-photon qudits. Without ancillary input photons, these passive measurements succeed with probability \(1-d^{-1}\), with all failures confined to the diagonal logical subspace. We show that identical single-mode squeezers applied to the \(2d\) interferometer outputs before photon-number-resolving detection recover part of this structured failure sector. Photon-number parity preserves the successful off-diagonal fusion signatures, while selected all-even patterns yield POVM elements proportional to definite pairwise Bell projectors. We derive the exact logical-space POVM and prove that a diagonal pattern is accepted if and only if its photon-number-imbalance vector has exactly two nonzero components of equal magnitude. The resulting closed elliptic-integral expression increases the ideal success probability, for instance, from \(75\%\) to \(79.62\%\) for \(d=4\), and from \(83.33\%\) to \(87.15\%\) for \(d=6\). With a representative finite detector saturation threshold, \(n_{\rm sat}=7\), the respective certified values remain \(78.84\%\) and \(86.71\%\). These results establish active Gaussian processing as a method for recycling structured measurement failures without ancillary input photons, at the cost of \(2d\) squeezing operations and a larger photon-number range at detection. △ Less

Submitted 28 June, 2026; originally announced June 2026.

Comments: Comments are welcome!

Differential Spectral Damping Gap Adaptive Regularization for Ill-Conditioned Kernel Methods

Authors: Praveg Vashishtha

Abstract: Kernel methods requiring matrix inversion -- particularly Least-Squares Twin Support Vector Machines (LSTSVM) -- suffer from exponential eigenvalue decay in their system matrices, producing severely ill-conditioned problems where standard Tikhonov regularization applies uniform damping regardless of eigenvector reliability. We propose Differential Spectral D… ▽ More Kernel methods requiring matrix inversion -- particularly Least-Squares Twin Support Vector Machines (LSTSVM) -- suffer from exponential eigenvalue decay in their system matrices, producing severely ill-conditioned problems where standard Tikhonov regularization applies uniform damping regardless of eigenvector reliability. We propose Differential Spectral Damping (DSD), a regularization formula that adapts its penalty to localized eigengap structure: preserving eigenvectors with large spectral gaps (reliable per Davis-Kahan perturbation theory) while aggressively suppressing those with small gaps (directionally corrupted beyond recovery). We motivate DSD through a principled design procedure grounded in the Davis-Kahan $\sin(Θ)$ theorem, systematically deriving the requirements for a reliability-aware damping function and selecting the exponential form for its smoothness, differentiability, and natural saturation properties. Through rigorous paired testing with fairly optimized baselines (including gradient-optimized Tikhonov receiving equal optimization opportunity), we demonstrate that DSD improves LSTSVM classification accuracy by +4.8 percentage points on real-world GINA ($d=970$, Cohen's $d = 4.49$, $p < 0.0001$), +10.4 percentage points at $d=200$, and +2.6 percentage points on Madelon ($d=500$) -- all using only principled spectral initialization while Tikhonov receives grid search. For pre-image reconstruction on manifold data, DSD ties Tikhonov at high perturbation noise ($p=0.99$) but slightly underperforms at lower noise levels; both reduce naive inversion error by $66\times$. We characterize the precise operating regime ($d \geq 100$, condition number $> 10^3$) and document where simpler methods suffice, providing practitioners with clear deployment guidance. △ Less

Submitted 22 June, 2026; originally announced June 2026.

Comments: 11 pages, 3 tables, 1 figure. Complete source code and experiments are available at https://github.com/Praveg432/dsd-regularization

Beamforming and RIS-Aided Ambient Backscatter Communications with Residual-Feature SVM Detection

Authors: Aobakwe Makgarapa, Burhan Wafai, Sangarapillai Lambotharan, Mahsa Derakhshani

Abstract: …a multi-antenna reader applies receive beamforming to steer toward the RF source and the tag separately. At the reader, a hypothesis-based minimum mean square error (MMSE) equalizer reconstructs the ambient symbol under each candidate tag state and produces a pair of residual features, which are classified by a support… ▽ More Ambient backscatter communication (AmBC) enables battery-free connectivity by modulating data onto existing radio-frequency (RF) signals, eliminating the need for dedicated power sources. However, its reliability degrades when direct wireless channels are obstructed or severely faded. Reconfigurable intelligent surfaces (RISs) offer a solution by creating a favorable propagation environment through the control of the phases of incident signals, thereby strengthening wireless links. This paper investigates an RIS-aided AmBC system that jointly exploits physical-layer reconfiguration and statistical learning to restore detection reliability under such conditions. The RIS phase profile is aligned for the source-RIS-tag link, while a multi-antenna reader applies receive beamforming to steer toward the RF source and the tag separately. At the reader, a hypothesis-based minimum mean square error (MMSE) equalizer reconstructs the ambient symbol under each candidate tag state and produces a pair of residual features, which are classified by a support vector machine (SVM) with a Gaussian kernel. We make the physical-layer-to-learning coupling explicit, i.e., RIS phase alignment and beamforming improve the signal-to-interference-plus-noise ratio (SINR), thereby rendering the residual features more separable and reducing classification error. Simulation results show that the proposed RIS-beamforming-SVM detector achieves substantial bit-error-rate (BER) gains over RIS-energy, SVM, and SVM-beamforming baselines across a wide SINR range, that the spectral-efficiency gains are governed more strongly by the number of RIS elements than by the number of reader antennas, and that performance saturates with a moderate RIS size, allowing near-optimal operation at reduced hardware cost. △ Less

Submitted 17 June, 2026; originally announced June 2026.

The alternating compositions of weighted differential operators yield the weights' Wronskian with which constant?

Authors: Kian C. Shah, Arthemy V. Kiselev

Abstract: …of the Lie bracket for two vector fields fixes $\mathrm{const}(1)=1$, and $\mathrm{const}(2)=2$ is found easily by hand; $\mathrm{const}(3)=90$ can still be obtained symbolically. The problem is to determine $\mathrm{const}(p\geqslant4)$. We compute $\mathrm{const}(p)$ exactly for all $p\leqslant14$ -- a 241-digit integer at $p=14$ -- and record the resul… ▽ More The alternated composition of $N=2p$ differential operators $w_j(x)\,\partial_x^p$ of strict order $p$ on the line $\mathbb{R}\ni x$ is again a differential operator of strict order $p$; its coefficient is the constant $\mathrm{const}(p)$, depending only on the arity $N$, times the Wronskian determinant of the originally taken coefficients $w_1,\dots,w_N$. The case $p=1$ of the Lie bracket for two vector fields fixes $\mathrm{const}(1)=1$, and $\mathrm{const}(2)=2$ is found easily by hand; $\mathrm{const}(3)=90$ can still be obtained symbolically. The problem is to determine $\mathrm{const}(p\geqslant4)$. We compute $\mathrm{const}(p)$ exactly for all $p\leqslant14$ -- a 241-digit integer at $p=14$ -- and record the resulting integer sequence as OEIS A392714. We prove that $v_p(\mathrm{const}(p))\geqslant p-1$ for every prime $p$, matching the exact equality observed numerically throughout our range, and conjecture that this equality holds in general. We show that $\log\mathrm{const}(p)$ grows like $αp^2\log p$, with the leading coefficient close to $2$, nearly saturating the bound $p^2\log p\,(1+O(1/\log p))\leqslant\log\mathrm{const}(p)\leqslant2p^2\log p\,(1+O(1/\log p))$ obtained by O. Zaboronski (private communication). A naturally arising reduced constant is found to decay to zero super-exponentially rather than grow, a direct consequence of this near-saturation. △ Less

Submitted 16 July, 2026; v1 submitted 11 May, 2026; originally announced May 2026.

Comments: 22 pages, 3 figures, 3 appendices

MSC Class: 15A15; 05E18; 05A10 (Primary) 05E16; 05A16 (Secondary)

LLM-Guided Strategy Synthesis for Scalable Equality Saturation

Authors: Chenyun Yin, Youwei Xiao, Yuze Luo, Yuyang Zou, Yun Liang

Abstract: Equality… ▽ More Equality saturation (EqSat) is a powerful optimization paradigm that compactly represents many equivalent programs in an e-graph and delays commitment until extraction selects a lowest-cost program. Making EqSat effective, therefore, requires not only domain-specific rewrite rules but also domain-specific strategies. Today, much of this strategy design is still manual, making it a major obstacle to automating e-graph-based compilers. Recent rule-synthesis frameworks can automatically infer large rewrite vocabularies from semantic specifications, but they also enlarge the rewrite space and further exacerbate e-graph explosion. Although large language models (LLMs) make automated strategy synthesis plausible, directly evolving backend code remains ineffective in practice. The search lacks reusable strategy abstractions and actionable feedback, and can easily trigger e-graph explosion or converge to poor designs. We present EggMind, an LLM-guided, end-to-end framework for synthesizing reusable EqSat strategies. At its core, EggMind introduces a domain-specific language, EqSatL, to represent EqSat strategies as explicit and inspectable artifacts. It then proposes an LLM-guided agentic workflow, equipped with novel techniques including proof-derived rewrite motif caching and tractability guidance, to search efficiently for high-quality strategies while keeping synthesis stable under e-graph growth. Evaluation shows that EggMind substantially improves the resource-quality trade-off on vectorization benchmarks, reducing final cost by 45.1% and peak RAM by 69.1% relative to full EqSat. We further show that the same methodology transfers effectively to an XLA-based tensor compiler, and demonstrate its practical potential in a logic-synthesis case study with augmented rewrite spaces. △ Less

Submitted 19 April, 2026; originally announced April 2026.

Hierarchical filtrations of vector bundles and birational geometry

Authors: Rahim Rahmati-asghar

Abstract: We introduce and systematically study \emph{hierarchical filtrations} of vector bundles on smooth projective varieties. These are filtrations by… ▽ More We introduce and systematically study \emph{hierarchical filtrations} of vector bundles on smooth projective varieties. These are filtrations by saturated subsheaves of equal rank whose successive quotients are torsion sheaves supported in codimension one. The associated numerical invariant, called \emph{hierarchical depth}, measures the maximal length of such filtrations. We establish general bounds for hierarchical depth in terms of the determinant class and provide exact formulas for smooth curves and varieties of Picard rank one. A key technical result concerns the commutativity of elementary transforms along disjoint divisors and their role in constructing filtrations. For surfaces, we analyze the behavior of hierarchical depth under birational morphisms and prove that it transforms additively along the steps of the minimal model program. In particular, we obtain an explicit formula relating the depth on a surface to that on its minimal model via exceptional divisor contributions. As an application, we connect hierarchical depth to degeneracies in algebraic--geometric codes and show that birational simplification via the MMP leads to effective improvements of code parameters. This establishes hierarchical depth as a new bridge between birational geometry, vector bundle theory, and coding theory. △ Less

Submitted 29 December, 2025; v1 submitted 21 December, 2025; originally announced December 2025.

Comments: 31 pages. Comments welcome

MSC Class: primary; 14G50; Secondary; 14C20; 14H52

Entropy-Rank Ratio: A Novel Entropy-Based Perspective for DNA Complexity and Classification

Authors: Emmanuel Pio Pastore, Giuseppe Passarino, Peppino Sapia, Francesco De Rango

Abstract: Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which positions a target sequence within the full distribution of all possible sequences of the same length by computing the proport… ▽ More Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which positions a target sequence within the full distribution of all possible sequences of the same length by computing the proportion of sequences that have an entropy value equal to or lower than that of the target. In other words, R expresses the relative position of a sequence within the global entropy spectrum, assigning values close to 0 for highly ordered sequences and close to 1 for highly disordered ones. DNA sequences are partitioned into fixed-length subsequences and non-overlapping n-mer groups; frequency vectors become ordered integer partitions and a combinatorial framework is used to derive the complete entropy distribution. Unlike classical measures, R is a normalized, distribution-aware measure bounded in [0,1] at fixed (T,n), which avoids saturation to log2 4 and makes values comparable across sequences under the same settings. We integrate R into data augmentation for convolutional neural networks by proposing ratio-guided cropping techniques and benchmark them against random, entropy-based, and compression-based methods. On two independent datasets, viral genes and human genes with polynucleotide expansions, models augmented via R achieve substantial gains in classification accuracy using extremely lightweight architectures. △ Less

Submitted 7 November, 2025; originally announced November 2025.

Comments: 31 pages, 10 figures

The Algorithmic Geometry of Decompression Schedules

Authors: Benjamin Marsh

Abstract: …gives a forward state sweep and a backward adjoint sweep, on-gassing holds are dominated, and the one compartment problem has closed form scalarised and capped solutions. For saturation decompression rectangular uncertainty collapses to one worst case endpoint, while finite bounce exposures admit a unique strictly interior worst rate with closed form locatio… ▽ More We cast decompression planning as hybrid optimal control with ppO$_2$ and narcotic depth feasibility, affine tissue ceilings, and convex oversaturation penalties. A rearrangement theorem gives monotone ascent for terminal objectives. Admitting excursions below the start depth breaks this, a one compartment instance with integrated oversaturation makes re-descent strictly beat every monotone profile, so monotone ascent is only an operational constraint. Without cumulative oxygen exposure the minimum inert feasible gas dominates every pure or relaxed policy along each fixed depth path, giving exact pure attainment with finitely many switches. A CNS/OTU oxygen budget is the path coupling state that restores gas choice and prevents zero inert holds, we derive its oxygen shadow price and gas switching inequality, and a risk price threshold makes no-stop ascent globally optimal. For fixed stops an exact dwell switching identity gives a forward state sweep and a backward adjoint sweep, on-gassing holds are dominated, and the one compartment problem has closed form scalarised and capped solutions. For saturation decompression rectangular uncertainty collapses to one worst case endpoint, while finite bounce exposures admit a unique strictly interior worst rate with closed form location and finitely many critical rates. Clipped oversaturation is not Markov, but full tissue vectors support safe dominance and one sided enclosures certify a hard cap. The finite menu problem is NP-hard with one tissue and has $2^m$ nondominated labels at bounded horizon, yet for fixed tissue dimension and polynomial conditioning, state compression gives an FPTAS for scalarisation and risk repair its exact cap counterpart. A frontier conjugacy theorem characterises which capped points scalarisation recovers, and worked examples match the dwell law, saturation endpoint equality, and time/risk frontier. △ Less

Submitted 21 July, 2026; v1 submitted 20 October, 2025; originally announced October 2025.

Trajectory tracking control of USV with actuator constraints in the presence of disturbances

Authors: Ram Milan Kumar Verma, Shashi Ranjan Kumar, Hemendra Arya

Abstract: …of finite control capability, which can notably degrade the performance if not properly addressed. Since actuator input bounds are typically known, integrating actuator saturation considerations into the control law design process can lead to enhanced performance and more precise trajectory tracking. Also, the actuators cannot provide the demanded forces or… ▽ More All practical systems often pose a problem of finite control capability, which can notably degrade the performance if not properly addressed. Since actuator input bounds are typically known, integrating actuator saturation considerations into the control law design process can lead to enhanced performance and more precise trajectory tracking. Also, the actuators cannot provide the demanded forces or torques instantaneously; hence, there is a limitation on the rate of magnitude. This work proposes nonlinear feedback controller designs developed using the Lyapunov stability and backstepping method while actively considering the actuator magnitude and rate constraints. The system dynamics are augmented with a smooth control input saturation model. Additionally, an observer is incorporated to estimate the disturbance vector. Through Lyapunov stability analysis, we demonstrate the system's stability under the proposed controller for the Uncrewed Surface Vessel (USV), ensuring adherence to actuator constraints provided their initial values fall within the prescribed bounds. Extensive numerical simulations performed by considering various trajectories and multiple initial conditions demonstrate the effectiveness of the controller in maintaining tracking performance without violating actuator constraints. This work also relaxes the assumption of equally capable actuators to be used to control the motion of USVs, affirming the viability of the controller in practical applications. △ Less

Submitted 20 June, 2025; originally announced June 2025.

Entanglement in the full state vector of boson sampling

Authors: Yulong Qiao, Joonsuk Huh, Frank Grossmann

Abstract: The full state vector of boson sampling is generated by passing S single photons through beam splitters of M modes. The initial Fock state is expressed withgeneralized coherent states, and an exact application of the unitary evolution becomes possible. Due to the favorable polynomial scaling in M , we can investigate Renyi entanglement entropies for moderate… ▽ More The full state vector of boson sampling is generated by passing S single photons through beam splitters of M modes. The initial Fock state is expressed withgeneralized coherent states, and an exact application of the unitary evolution becomes possible. Due to the favorable polynomial scaling in M , we can investigate Renyi entanglement entropies for moderate particle and huge mode numbers. We find (almost) Renyi index independent symmetric Page curves with maximum entropy at equal partition. Furthermore, the maximum entropy as a function of mode index saturates as a function of M in the collision-free subspace case. The asymptotic value of the entropy increases linearly with S. Furthermore, we show that the build-up of the entanglement leads to a cusp at subsystem size equal to S in the asymmetric entanglement curve. The maximum entanglement is reached surprisingly early before the mode population is distributed over the whole system. △ Less

Submitted 19 April, 2023; v1 submitted 18 October, 2022; originally announced October 2022.

Journal ref: SciPost Phys. 15, 007 (2023)

Sensitivity of Au+Au collisions to the symmetric nuclear matter equation of state at 2 -- 5 nuclear saturation densities

Authors: Dmytro Oliinychenko, Agnieszka Sorensen, Volker Koch, Larry McLerran

Abstract: …ranging from 1 to 20 GeV per nucleon in the fixed target frame can be used for an accurate determination of the symmetric nuclear matter equation of state at baryon densities equal 2--4 times nuclear saturation density $n_0$. We simulate Au+Au collisions at these energies using a hadronic transport model with an adjust… ▽ More We demonstrate that proton and pion flow measurements in heavy-ion collisions at incident energies ranging from 1 to 20 GeV per nucleon in the fixed target frame can be used for an accurate determination of the symmetric nuclear matter equation of state at baryon densities equal 2--4 times nuclear saturation density $n_0$. We simulate Au+Au collisions at these energies using a hadronic transport model with an adjustable vector mean-field potential dependent on baryon density $n_B$. We show that the mean field can be parametrized to reproduce a given density-dependence of the speed of sound at zero temperature $c_s^2(n_B, T = 0)$, which we vary independently in multiple density intervals to probe the differential sensitivity of heavy-ion observables to the equation of state at these specific densities. Recent flow data from the STAR experiment at the center-of-mass energies $\sqrt{s_{NN}} = \{3.0, 4.5 \}\ $ GeV can be described by our model, and a Bayesian analysis of these data indicates a hard equation of state at $n_B \in (2,3) n_0$ and a possible phase transition at $n_B \in (3,4) n_0$. More data at $\sqrt{s_{NN}} = 2-5$ GeV, as well as a more thorough analysis of the model systematic uncertainties will be necessary for a more precise conclusion. △ Less

Submitted 25 September, 2023; v1 submitted 25 August, 2022; originally announced August 2022.

Comments: 26 pages, 18 figures, accepted to publication in Phys Rev C, minor fixes

Sketch-Guided Equality Saturation: Scaling Equality Saturation to Complex Optimizations of Functional Programs

Authors: Thomas Koehler, Phil Trinder, Michel Steuwer

Abstract: …to define and explore optimization spaces. However, deciding what sequence of rewrites to apply is hard and has a huge impact on the performance of the rewritten program. Equality… ▽ More Generating high-performance code for diverse hardware and application domains is challenging. Functional array programming languages with patterns like map and reduce have been successfully combined with term rewriting to define and explore optimization spaces. However, deciding what sequence of rewrites to apply is hard and has a huge impact on the performance of the rewritten program. Equality saturation avoids the issue by exploring many possible ways to apply rewrites, efficiently representing many equivalent programs in an e-graph data structure. Equality saturation has some limitations when rewriting functional language terms, as currently naive encodings of the lambda calculus are used. We present new techniques for encoding polymorphically typed lambda calculi, and show that the efficient encoding reduces the runtime and memory consumption of equality saturation by orders of magnitude. Moreover, equality saturation does not yet scale to complex compiler optimizations. These emerge from long rewrite sequences of thousands of rewrite steps, and may use pathological combinations of rewrite rules that cause the e-graph to quickly grow too large. This paper introduces \emph{sketch-guided equality saturation}, a semi-automatic technique that allows programmers to provide program sketches to guide rewriting. Sketch-guided equality saturation is evaluated for seven complex matrix multiplication optimizations, including loop blocking, vectorization, and multi-threading. Even with efficient lambda calculus encoding, unguided equality saturation can locate only the two simplest of these optimizations, the remaining five are undiscovered even with an hour of compilation time and 60GB of RAM. By specifying three or fewer sketch guides all seven optimizations are found in seconds of compilation time, using under 1GB of RAM, and generating high performance code. △ Less

Submitted 3 June, 2022; v1 submitted 25 November, 2021; originally announced November 2021.

Comments: 23 pages excluding references, submitted to OOPLSA 2022

Motion Control of Redundant Robots with Generalised Inequality Constraints

Authors: Amirhossein Kazemipour, Maram Khatib, Khaled Al Khudir, Alessandro De Luca

Abstract: We present an improved version of the Saturation in the Null Space (SNS) algorithm for redundancy resolution at the velocity level. In addition to hard bounds on joint space motion, we consider also Cartesian box constraints that cannot be violated at any time. The modified algorithm combines all bounds into a single augmented generalised… ▽ More We present an improved version of the Saturation in the Null Space (SNS) algorithm for redundancy resolution at the velocity level. In addition to hard bounds on joint space motion, we consider also Cartesian box constraints that cannot be violated at any time. The modified algorithm combines all bounds into a single augmented generalised vector and gives equal, highest priority to all inequality constraints. When needed, feasibility of the original task is enforced by the SNS task scaling procedure. Simulation results are reported for a 6R planar robot. △ Less

Submitted 4 October, 2021; originally announced October 2021.

Comments: 3 pages, 4 figures, 2021 Italian Conference on Robotics and Intelligent Machines (2021 I-RIM)

Exchange interaction, disorder, and stacking faults in rhombohedral graphene multilayers

Authors: James H. Muten, Alex J. Copeland, Edward McCann

Abstract: …in bilayer graphene to thin films of rhombohedral graphite with up to thirty layers. For the ground state, the order parameter (the separation of bands at the valley center) saturates to a constant non-zero value as the layer number increases, whereas the band gap decreases with layer number. We consider chiral symmetry breaking disorder in the form of rando… ▽ More We apply the mean-field Hartree Fock theory of gapped electronic states at charge neutrality in bilayer graphene to thin films of rhombohedral graphite with up to thirty layers. For the ground state, the order parameter (the separation of bands at the valley center) saturates to a constant non-zero value as the layer number increases, whereas the band gap decreases with layer number. We consider chiral symmetry breaking disorder in the form of random layer potentials and chiral preserving disorder in the form of random values of the interlayer coupling. The former reduces the magnitude of the mean band gap whereas the latter has a negligible effect, which is due to self-averaging within a film with a large number of layers. We determine the ground state in the presence of an individual stacking fault which results in two pairs of low-energy bands and we identify two separate order parameters. One of them determines the band gap at zero temperature, the other determines the critical temperature leading, overall, to a temperature dependence of the band gap that is distinct to that of pristine rhombohedral graphite. In the presence of stacking faults, each individual rhombohedral section with $m$ layers contributes a pair of low-energy flat bands producing a peak in the Berry curvature located at a characteristic $m$-dependent wave vector. The Chern number per spin-valley flavor for the filled valence bands in the ground state is equal in magnitude to the total number of layers divided by two, the same value as for pristine rhombohedral graphite. △ Less

Submitted 6 July, 2021; v1 submitted 26 February, 2021; originally announced February 2021.

Comments: 16 pages, 15 figures

Journal ref: Phys. Rev. B 104, 035404 (2021)

Truncated Linear Regression in High Dimensions

Authors: Constantinos Daskalakis, Dhruv Rohatgi, Manolis Zampetakis

Abstract: …whose dependent variable equals $y_i= A_i^{\rm T} \cdot x^* + η_i$, where $x^*$ is some fixed unknown vector of interest and $η_i$ is independent noise; except we are only given an observation if its dependent variable $y_i$ lies in some "truncation set" $S \subset \mathbb{R}$. The goal is to recover $x^*$ und… ▽ More As in standard linear regression, in truncated linear regression, we are given access to observations $(A_i, y_i)_i$ whose dependent variable equals $y_i= A_i^{\rm T} \cdot x^* + η_i$, where $x^*$ is some fixed unknown vector of interest and $η_i$ is independent noise; except we are only given an observation if its dependent variable $y_i$ lies in some "truncation set" $S \subset \mathbb{R}$. The goal is to recover $x^*$ under some favorable conditions on the $A_i$'s and the noise distribution. We prove that there exists a computationally and statistically efficient method for recovering $k$-sparse $n$-dimensional vectors $x^*$ from $m$ truncated samples, which attains an optimal $\ell_2$ reconstruction error of $O(\sqrt{(k \log n)/m})$. As a corollary, our guarantees imply a computationally efficient and information-theoretically optimal algorithm for compressed sensing with truncation, which may arise from measurement saturation effects. Our result follows from a statistical and computational analysis of the Stochastic Gradient Descent (SGD) algorithm for solving a natural adaptation of the LASSO optimization problem that accommodates truncation. This generalizes the works of both: (1) [Daskalakis et al. 2018], where no regularization is needed due to the low-dimensionality of the data, and (2) [Wainright 2009], where the objective function is simple due to the absence of truncation. In order to deal with both truncation and high-dimensionality at the same time, we develop new techniques that not only generalize the existing ones but we believe are of independent interest. △ Less

Submitted 28 July, 2020; originally announced July 2020.

Comments: 30 pages, 1 figure

Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

Authors: Yin-Chen He, Junchen Rong, Ning Su

Abstract: …vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough $N>N_c(d)$ in a given dimension $d$. In thi… ▽ More It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of $O(N)$ vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough $N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks. The first case is the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2)_1$ Wess-Zumino-Witten (WZW) model, and all the $SU(2)_{k>2}$ WZW models saturate the numerical bound on the left side of the kink. We further carry out dimensional continuation of the 2d $SU(2)_1$ kink towards the 3d $SO(5)$ deconfined phase transition. We find the kink disappears at around $d=2.7$ dimensions indicating the $SO(5)$ deconfined phase transition is weakly first order. The second interesting observation is, the $O(2)$ bootstrap bound does not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the $N=\infty$ limit, where the non-WF kink sits at $(Δ_φ, Δ_T)=(d-1, 2d)$ in $d$ dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF CFTs originating from free boson at $N=\infty$. △ Less

Submitted 13 April, 2021; v1 submitted 8 May, 2020; originally announced May 2020.

Comments: 16+3 pages

Journal ref: SciPost Phys. 10, 115 (2021)

Comparative analysis of information measures of the Dirichlet and Neumann two-dimensional quantum dots

Authors: O. Olendski

Abstract: …of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where one-parameter momentum entropies exist is equal to 2/5 for the Dirichlet requirement and 2/3 for the Neumann one. Since their 1D counterparts are $1/4$ and $1/2$, respectively, this simultaneously reveals that this critical value crucially depends not only on the position BC but… ▽ More Analytic representation of both position as well as momentum waveforms of the two-dimensional (2D) circular quantum dots with the Dirichlet and Neumann boundary conditions (BCs) allowed an efficient computation in either space of Shannon $S$, Rényi $R(α)$ and Tsallis $T(α)$ entropies, Onicescu energies $O$ and Fisher informations $I$. It is shown that a transition to the 2D geometry lifts the 1D degeneracy of the position components $S_ρ$, $O_ρ$, $R_ρ(α)$. Among many other findings, it is established that the lower limit $α_{TH}$ of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where one-parameter momentum entropies exist is equal to 2/5 for the Dirichlet requirement and 2/3 for the Neumann one. Since their 1D counterparts are $1/4$ and $1/2$, respectively, this simultaneously reveals that this critical value crucially depends not only on the position BC but the dimensionality of the structure too. As the 2D Neumann threshold $α_{TH}^N$ is greater than one half, its Rényi uncertainty relation for the sum of the position and wave vector components $R_ρ(α)+R_γ\left(\fracα{2α-1}\right)$ is valid in the range $[1/2,2)$ only with its logarithmic divergence at the right edge whereas for all other systems it is defined at any coefficient $α$ not smaller than one half. For both configurations, the lowest-energy level at $α=1/2$ does saturate Rényi and Tsallis entropic inequalities. Other properties are discussed and analyzed from the mathematical and physical points of view. △ Less

Submitted 12 January, 2021; v1 submitted 19 June, 2018; originally announced June 2018.

Journal ref: Int. J. Quantum Chem. vol. 121, e26455 (2021)

The uncertainty principle and the energy identity for holomorphic maps in geometric quantum mechanics

Authors: Barbara A. Sanborn

Abstract: …-holomorphic curves. We consider a family of maps from a Riemann surface into a finite-dimensional quantum state space by using the vector fields generated by two quantum observables,and show that the Fubini-Study metric tensor pulls back by such a map to the covariance tensor for the two observables. By calculating the map energy density in the pull-back me… ▽ More The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure. This paper extends the geometric quantum theory to include aspects of the symplectic topology of the state space by identifying the Robertson-Schrödinger uncertainty relation for pure quantum states as the differential version of the energy identity in the theory of $J$-holomorphic curves. We consider a family of maps from a Riemann surface into a finite-dimensional quantum state space by using the vector fields generated by two quantum observables,and show that the Fubini-Study metric tensor pulls back by such a map to the covariance tensor for the two observables. By calculating the map energy density in the pull-back metric, the uncertainty relation is represented as an equality that compares the map energy differential to the sum of the pull-back of the symplectic form and a positive definite term that vanishes when the map is holomorphic. Saturation of the Robertson-Schrödinger inequality occurs when the map is conformal and the off-diagonal covariance terms vanish. For compact Riemann surfaces where such a map can be globally defined, if the map is holomorphic, it is harmonic and its image is a minimal surface. In this case, the uncertainty product integral is a topological invariant that depends only on the homology class of the curve modulo its boundary. △ Less

Submitted 25 October, 2017; originally announced October 2017.

Comments: 13 pages

From log-determinant inequalities to Gaussian entanglement via recoverability theory

Authors: Ludovico Lami, Christoph Hirche, Gerardo Adesso, Andreas Winter

Abstract: Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields \begin{equation*} \ln\det V_{AC} + \ln\det V_{BC} - \ln\det V_{ABC} - \ln\det V_C \geq 0 \end{equation*} for all… ▽ More Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields \begin{equation*} \ln\det V_{AC} + \ln\det V_{BC} - \ln\det V_{ABC} - \ln\det V_C \geq 0 \end{equation*} for all $3\times 3$-block matrices $V_{ABC}$, where subscripts identify principal submatrices. We shall refer to the above inequality as SSA of log-det entropy. In this paper we develop further insights on the properties of the above inequality and its applications to classical and quantum information theory. In the first part of the paper, we show how to find known and new necessary and sufficient conditions under which saturation with equality occurs. Subsequently, we discuss the role of the classical transpose channel (also known as Petz recovery map) in this problem and find its action explicitly. We then prove some extensions of the saturation theorem, by finding faithful lower bounds on a log-det conditional mutual information. In the second part, we focus on quantum Gaussian states, whose covariance matrices are not only positive but obey additional constraints due to the uncertainty relation. For Gaussian states, the log-det entropy is equivalent to the Rényi entropy of order $2$. We provide a strengthening of log-det SSA for quantum covariance matrices that involves the so-called Gaussian Rényi-$2$ entanglement of formation, a well-behaved entanglement measure defined via a Gaussian convex roof construction. We then employ this result to define a log-det entropy equivalent of the squashed entanglement, which is remarkably shown to coincide with the Gaussian Rényi-$2$ entanglement of formation. This allows us to establish useful properties of such measure(s), like monogamy, faithfulness, and additivity on Gaussian states. △ Less

Submitted 3 November, 2017; v1 submitted 17 March, 2017; originally announced March 2017.

Comments: 17 pages; v2 has many typos corrected and it is close to the published version (IEEE)

Journal ref: IEEE Trans. Inf. Theory, vol. 63, no. 11, pp. 7553-7568 (2017)

Stably stratified turbulence in the presence of large-scale forcing

Authors: C. Rorai, P. D. Mininni, A. Pouquet

Abstract: We perform two high resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re~25000 and Froude number respectively of Fr~0.1 and Fr~0.03. The flows are forced at large scale and discretized on an isotropic grid of 2048^3 points. Stratification makes the flow anisotropic and introduces two extra characteristic scales wit… ▽ More We perform two high resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re~25000 and Froude number respectively of Fr~0.1 and Fr~0.03. The flows are forced at large scale and discretized on an isotropic grid of 2048^3 points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, L_B, and the Ozmidov scale, l_{oz}. The former is related to the number of layers that the flow develops in the direction of gravity, the latter is regarded as the scale at which isotropy is recovered. The values of L_B and l_{oz} depend on the Froude number and their absolute and relative size affect the repartition of energy among Fourier modes. By contrasting the behavior of the two simulated flows we identify some surprising similarities: after an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy, and energy dissipation rate. Further similarities emerge at large scales: the same ratio between potential and total energy (~0.1) is spontaneously selected by the flows, and slow modes grow monotonically in both regimes causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a ~ k^{-3} parallel spectrum develops for the Fr ~ 0.03 run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until L_B, as observed in the nocturnal planetary boundary layer. △ Less

Submitted 3 December, 2014; originally announced December 2014.

Mixed lipid bilayers with locally varying spontaneous curvature and bending

Authors: Guillaume Gueguen, Nicolas Destainville, Manoel Manghi

Abstract: …, and a bending modulus equal to $κ_0+κ_1(ψ_1+ψ_2)/2$. This model allows us to define curved patches as membrane domains where the asymmetry in composition, $ψ_1-ψ_2$, is large, and thick and stiff patches where $ψ_1+ψ_2$ is large. These thick patches are good candidates for being lipidic rafts, as observed in cell membranes, which are composed primarily of… ▽ More A model of lipid bilayers made of a mixture of two lipids with different average compositions on both leaflets, is developed. A Landau hamiltonian describing the lipid-lipid interactions on each leaflet, with two lipidic fields $ψ_1$ and $ψ_2$, is coupled to a Helfrich one, accounting for the membrane elasticity, via both a local spontaneous curvature, which varies as $C_0+C_1(ψ_1-ψ_2)/2$, and a bending modulus equal to $κ_0+κ_1(ψ_1+ψ_2)/2$. This model allows us to define curved patches as membrane domains where the asymmetry in composition, $ψ_1-ψ_2$, is large, and thick and stiff patches where $ψ_1+ψ_2$ is large. These thick patches are good candidates for being lipidic rafts, as observed in cell membranes, which are composed primarily of saturated lipids forming a liquid-ordered domain and are known to be thick and flat nano-domains. The lipid-lipid structure factors and correlation functions are computed for globally spherical membranes and planar ones. Phase diagrams are established, within a Gaussian approximation, showing the occurrence of two types of Structure Disordered phases, with correlations between either curved or thick patches, and an Ordered phase, corresponding to the divergence of the structure factor at a finite wave vector. The varying bending modulus plays a central role for curved membranes, where the driving force $κ_1C_0^2$ is balanced by the line tension, to form raft domains of size ranging from 10 to 100~nm. For planar membranes, raft domains emerge via the cross-correlation with curved domains. A global picture emerges from curvature-induced mechanisms, described in the literature for planar membranes, to coupled curvature- and bending-induced mechanisms in curved membranes forming a closed vesicle. △ Less

Submitted 27 August, 2014; v1 submitted 9 May, 2014; originally announced May 2014.

Journal ref: Eur. Phys. J. E (2014) 37: 76

Analytic cycles, Bott-Chern forms, and singular sets for the Yang-Mills flow on Kaehler manifolds

Authors: Benjamin Sibley, Richard A. Wentworth

Abstract: It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kaehler manifolds is completely determined by the Harder-Narasimhan-Seshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtratio… ▽ More It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kaehler manifolds is completely determined by the Harder-Narasimhan-Seshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves. We derive a singular Bott-Chern formula relating the second Chern form of a smooth metric on the bundle to the Chern current of an admissible metric on the associated graded sheaf. This is used to show that the multiplicities of the top dimensional bubbling locus defined via the Yang-Mills density agree with the corresponding multiplicities for the Harder-Narasimhan-Seshadri filtration. The set theoretic equality of singular sets is a consequence. △ Less

Submitted 28 September, 2018; v1 submitted 16 February, 2014; originally announced February 2014.

Comments: Lemma 4.2 has been replaced with a more general argument based on Scheja's theorem. Erratum added

Journal ref: Advances in Mathematics 279 (2015), 501-531

Nuclear equation of state in a relativistic independent quark model with chiral symmetry and variation with quark masses

Authors: N. Barik, R. N. Mishra, D. K. Mohanty, P. K. Panda, T. Frederico

Abstract: …potential model; where the dominant confining interaction for the free independent quarks inside a nucleon, is represented by a phenomenologically average potential in equally mixed scalar-… ▽ More We have calculated the properties of nuclear matter in a self-consistent manner with quark-meson coupling mechanism incorporating structure of nucleons in vacuum through a relativistic potential model; where the dominant confining interaction for the free independent quarks inside a nucleon, is represented by a phenomenologically average potential in equally mixed scalar-vector harmonic form. Corrections due to spurious centre of mass motion as well as those due to other residual interactions such as the one gluon exchange at short distances and quark-pion coupling arising out of chiral symmetry restoration; have been considered in a perturbation manner to obtain the nucleon mass in vacuum. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to sigma and omega mesons through mean field approximations. The relevant parameters of the interaction are obtained self consistently while realizing the saturation properties such as the binding energy, pressure and compressibility of the nuclear matter. We also discuss some implications of chiral symmetry in nuclear matter along with the nucleon and nuclear sigma term and the sensitivity of nuclear matter binding energy with variations in the light quark mass. △ Less

Submitted 3 July, 2013; originally announced July 2013.

Comments: 14 pages, 15 figures, accepted in Phys. Rev. C

Interaction-induced charge and spin pumping through a quantum dot at finite bias

Authors: Hernan L. Calvo, Laura Classen, Janine Splettstoesser, Maarten R. Wegewijs

Abstract: …and relate these to the concepts of charge and spin emissivities previously discussed within the time-dependent scattering matrix approach. Expressed in terms of auxiliary vector fields, the response coefficients allow for a straightforward analysis of recently predicted interaction-induced pumping under periodic modulation of the gate and bias voltage [Phys… ▽ More We investigate charge and spin transport through an adiabatically driven, strongly interacting quantum dot weakly coupled to two metallic contacts with finite bias voltage. Within a kinetic equation approach, we identify coefficients of response to the time-dependent external driving and relate these to the concepts of charge and spin emissivities previously discussed within the time-dependent scattering matrix approach. Expressed in terms of auxiliary vector fields, the response coefficients allow for a straightforward analysis of recently predicted interaction-induced pumping under periodic modulation of the gate and bias voltage [Phys. Rev. Lett. 104, 226803 (2010)]. We perform a detailed study of this effect and the related adiabatic Coulomb blockade spectroscopy, and, in particular, extend it to spin pumping. Analytic formulas for the pumped charge and spin in the regimes of small and large driving amplitude are provided for arbitrary bias. In the absence of a magnetic field, we obtain a striking, simple relation between the pumped charge at zero bias and at bias equal to the Coulomb charging energy. At finite magnetic field, there is a possibility to have interaction-induced pure spin pumping at this finite bias value, and generally, additional features appear in the pumped charge. For large-amplitude adiabatic driving, the magnitude of both the pumped charge and spin at the various resonances saturate at values which are independent of the specific shape of the pumping cycle. Each of these values provide an independent, quantitative measurement of the junction asymmetry. △ Less

Submitted 16 October, 2012; originally announced October 2012.

Comments: 17 pages, 8 figures

Journal ref: Phys. Rev. B 86, 245308 (2012)

Electric field generation by the electron beam filamentation instability: Filament size effects

Authors: M E Dieckmann, A Bret

Abstract: …with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially… ▽ More The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their nonrelativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated, that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied, that the electrostatic field performed undamped oscillations around a background electric field. Here we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF. △ Less

Submitted 9 November, 2009; originally announced November 2009.

Comments: 14 pages, 10 plots, accepted for publication in Physica Scripta

The filamentation instability driven by warm electron beams: Statistics and electric field generation

Authors: M E Dieckmann

Abstract: …of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases… ▽ More The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow-aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation. △ Less

Submitted 1 October, 2009; originally announced October 2009.

Comments: 10 pages, 6 figures, accepted by the Plasma Physics and Controlled Fusion (Special Issue EPS 2009)

PIC simulations of the Thermal Anisotropy-Driven Weibel Instability: Field growth and phase space evolution upon saturation

Authors: A Stockem, M E Dieckmann, R Schlickeiser

Abstract: …and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: A 2D simulation, with a simulation plane that includes the direction of higher temperature, demo… ▽ More The Weibel instability is investigated with PIC simulations of an initially unmagnetized and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: A 2D simulation, with a simulation plane that includes the direction of higher temperature, demonstrates that the wave spectrum is initially confined to one dimension. The electric field components in the simulation plane generated by the instability equalize at the end of the simulation through a secondary instability. A 1D PIC simulation with a high resolution, where the simulation box is aligned with the wave vectors of the growing waves, reveals details of the electron phase space distribution and permits a comparison of the magnetic and electric fields when the instability saturates. It is shown that the electrostatic field is driven by the magnetic pressure gradient and that it and the magnetic field redistribute the electrons in space. △ Less

Submitted 14 May, 2009; originally announced May 2009.

Comments: Plasma Phys Controll Fusion, in press (to appear in june 2009)

Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas

Authors: M E Dieckmann, P K Shukla, L Stenflo

Abstract: …beams of charged particles in plasmas is modelled by a particle-in-cell (PIC) simulation. Each beam consists of the electrons and positrons. The four species are equally dense and they have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity… ▽ More The filamentation instability driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell (PIC) simulation. Each beam consists of the electrons and positrons. The four species are equally dense and they have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a result no electrostatic field is generated by the magnetic field through its magnetic pressure gradient prior to its saturation. This electrostatic field would be repulsive at the centres of the filaments and limit the maximum charge and current density. The filaments of electrons and positrons in this simulation reach higher charge and current densities than in one with no positrons. The oscillations of the magnetic field strength induced by the magnetically trapped particles result in an oscillatory magnetic pressure gradient force. The latter interplays with the statistical fluctuations in the particle density and it probably enforces a charge separation, by which electrostatic waves grow after the filamentation instability has saturated. △ Less

Submitted 3 May, 2009; originally announced May 2009.

Comments: 13 pages, 8 figures

Journal ref: Plasma Phys. Control. Fusion 51 (2009) 065015

Saturable discrete vector solitons in one-dimensional photonic lattices

Authors: Rodrigo A. Vicencio, Eugene Smirnov, Christian E. Rüter, Detlef Kip, Milutin Stepić

Abstract: Localized vectorial modes, with equal frequencies and mutually orthogonal polarizations, are investigated both analytically and experimentally in a one-dimensional photonic lattice with… ▽ More Localized vectorial modes, with equal frequencies and mutually orthogonal polarizations, are investigated both analytically and experimentally in a one-dimensional photonic lattice with saturable nonlinearity. It is shown that these modes may span over many lattice elements and that energy transfer among the two components is both phase and intensity dependent. The transverse electrically polarized mode exhibits a single-hump structure and spreads in cascades in saturation, while the transverse magnetically polarized mode exhibits splitting into a two-hump structure. Experimentally such discrete vector solitons are observed in lithium niobate lattices for both coherent and mutually incoherent excitations. △ Less

Submitted 30 January, 2007; originally announced January 2007.

Comments: 4 pages, 5 figures (reduced for arXiv)

Journal ref: Phys. Rev. A 76, 033816 (2007).

Vector invariants in arbitrary characteristic

Authors: Frank D. Grosshans

Abstract: Let k be an algebraically closed field of characteristic p > 0. Let H be a subgroup of GL(n,k). We are interested in the determination of the vector invariants of H. When the characteristic of k is 0, it is known that the invariants of d… ▽ More Let k be an algebraically closed field of characteristic p > 0. Let H be a subgroup of GL(n,k). We are interested in the determination of the vector invariants of H. When the characteristic of k is 0, it is known that the invariants of d vectors, d > n, are obtained from those of n vectors by polarization. This result is not true when char k = p > 0 even in the case where H is a torus. However, we show that the algebra of invariants is always integral over the algebra of polarized invariants and when H is reductive is actually the p - root closure of that algebra. We also give conditions for the algebras to be equal, relating equality to good filtrations and saturated subgroups. We conclude with examples where H is finite or a classical group or is a certain kind of unipotent subgroup of GL(n,k). △ Less

Submitted 26 May, 2006; originally announced May 2006.

MSC Class: 13A50

Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces

Authors: F. Jugeau, H. Sazdjian

Abstract: The quark-antiquark gauge invariant Green function is studied through its dependence on Wilson loops. The latter are saturated, in the large Nc limit and for large contours, by minimal surfaces. A covariant bound state equation is derived which in the center-of-mass frame and at… ▽ More The quark-antiquark gauge invariant Green function is studied through its dependence on Wilson loops. The latter are saturated, in the large Nc limit and for large contours, by minimal surfaces. A covariant bound state equation is derived which in the center-of-mass frame and at equal-times takes the form of a Breit-Salpeter type equation. The large-distance interaction potentials reduce in the static case to a confining linear vector potential. In general, the interaction potentials involve contributions having the structure of flux tube like terms. △ Less

Submitted 12 October, 2005; originally announced October 2005.

Comments: 9 pages, 4 figures. Talk given by H.S. at the Workshop QCD at Work 2005, Conversano, Italy, 16-20 June 2005. To appear in the Proceedings (AIP)

Report number: IPNO-DR-05-06

Journal ref: AIPConf.Proc.806:238-244,2006

Exploring the nucleus in the context of low-energy QCD

Authors: Dario Vretenar, Wolfram Weise

Abstract: …combined with the large isoscalar nucleon self-energies that arise through changes in the quark condensate and the quark density at finite baryon density. Nuclear binding and saturation are almost completely generated by chiral (two-pion exchange) fluctuations in combination with Pauli effects, whereas strong scalar and… ▽ More These lecture notes address a central problem of theoretical nuclear physics: how to establish a relationship between low-energy, non-perturbative QCD and nuclear phenomenology which includes both nuclear matter and finite nuclei. We develop a microscopic covariant description of nuclear many-body dynamics constrained by chiral symmetry and in-medium QCD sum rules. A relativistic point-coupling model is derived, based on an effective Lagrangian with density-dependent contact interactions between nucleons. These interactions are constructed from chiral one- and two-pion exchange, combined with the large isoscalar nucleon self-energies that arise through changes in the quark condensate and the quark density at finite baryon density. Nuclear binding and saturation are almost completely generated by chiral (two-pion exchange) fluctuations in combination with Pauli effects, whereas strong scalar and vector fields of about equal magnitude and opposite sign, induced by changes of the QCD vacuum in the presence of baryonic matter, generate the large effective spin-orbit potential in finite nuclei. Promising results are found for the nuclear matter equation of state and for the bulk and single-nucleon properties of finite nuclei. △ Less

Submitted 5 December, 2003; originally announced December 2003.

Comments: 50 pages, 11 figures, invited lecture at 307. WE-Heraeus-Seminar, "Relativistic Structure Models for the Physics of Radioactive Nuclear Beams," May 12-16, 2003, Bad Honnef, Germany

Journal ref: Lect.Notes Phys. 641 (2004) 65-117

Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

Authors: P. Finelli, N. Kaiser, D. Vretenar, W. Weise

Abstract: …parameters and functional forms of density dependent couplings. It is shown that chiral (two-pion exchange) fluctuations play a prominent role for nuclear binding and saturation, whereas strong scalar and vector fields of about equal magnitude and opposite sign, induced by change… ▽ More We derive a microscopic relativistic point-coupling model of nuclear many-body dynamics constrained by in-medium QCD sum rules and chiral symmetry. The effective Lagrangian is characterized by density dependent coupling strengths, determined by chiral one- and two-pion exchange and by QCD sum rule constraints for the large isoscalar nucleon self-energies that arise through changes of the quark condensate and the quark density at finite baryon density. This approach is tested in the analysis of the equations of state for symmetric and asymmetric nuclear matter, and of bulk and single-nucleon properties of finite nuclei. In comparison with purely phenomenological mean-field approaches, the built-in QCD constraints and the explicit treatment of pion exchange restrict the freedom in adjusting parameters and functional forms of density dependent couplings. It is shown that chiral (two-pion exchange) fluctuations play a prominent role for nuclear binding and saturation, whereas strong scalar and vector fields of about equal magnitude and opposite sign, induced by changes of the QCD vacuum in the presence of baryonic matter, generate the large effective spin-orbit potential in finite nuclei. △ Less

Submitted 4 May, 2004; v1 submitted 17 July, 2003; originally announced July 2003.

Comments: 46 pages, 12 figures, uses elsart.cls, revised version, to appear in Nucl.Phys. A735 (2004) 449-481

Journal ref: Nucl.Phys. A735 (2004) 449-481

Bound state equation in the Wilson loop approach with minimal surfaces

Authors: F. Jugeau, H. Sazdjian

Abstract: The large-distance dynamics in quarkonium systems is investigated, in the large N limit, through the saturation of Wilson loop averages by minimal surfaces. Using a representation for the quark propagator in the presence of the external gluon field based on the use of path-ordered phase factors, a covariant three-dimensional bound state equation of the Breit… ▽ More The large-distance dynamics in quarkonium systems is investigated, in the large N limit, through the saturation of Wilson loop averages by minimal surfaces. Using a representation for the quark propagator in the presence of the external gluon field based on the use of path-ordered phase factors, a covariant three-dimensional bound state equation of the Breit-Salpeter type is derived, in which the interaction potentials are provided by the energy-momentum vector of the straight segment joining the quark to the antiquark and carrying a constant linear energy density, equal to the string tension. The interaction potentials are confining and reduce to the linear vector potential in the static case and receive, for moving quarks, contributions from the moments of inertia of the straight segment. The self-energy parts of the quark propagators induce spontaneous breakdown of chiral symmetry with a mechanism identical to that of the exchange of one Coulomb-gluon. The nonrelativistic and ultrarelativistic properties of the bound state spectrum are studied. △ Less

Submitted 2 May, 2003; originally announced May 2003.

Comments: 57 pages, 7 figures

Report number: IPNO-DR-03-02

Journal ref: Nucl.Phys. B670 (2003) 221-263

Rho-omega mixing in asymmetric nuclear matter via QCD sum rule approach

Authors: Abhee K. Dutt-Mazumder, Ralf Hofmann, Maxim Pospelov

Abstract: We evaluate the operator product expansion (OPE) for a mixed correlator of the isovector and isoscalar vector currents in the background of the nucleon density with intrinsic isospin asymmetry [i.e. excess of neutrons over protons] and match it with its imaginary part, given by resonances and continuum, via the dispersion relation. The leading density-depend… ▽ More We evaluate the operator product expansion (OPE) for a mixed correlator of the isovector and isoscalar vector currents in the background of the nucleon density with intrinsic isospin asymmetry [i.e. excess of neutrons over protons] and match it with its imaginary part, given by resonances and continuum, via the dispersion relation. The leading density-dependent contribution to $ρ-ω$ mixing is due the scattering term, which turns out to be larger than any density dependent piece in the OPE. We estimate that the asymmetric density of $n_n-n_p \sim 2.5 \times 10^{-2} ~{\rm fm^3}$ induces the amplitude of $ρ-ω$ mixing, equal in magnitude to the mixing amplitude in vacuum, with the constructive interference for positive and destructive for negative values of $n_n-n_p$. We revisit sum rules for vector meson masses at finite nucleon density to point out the numerical importance of the screening term in the isoscalar channel, which turns out to be one order of magnitude larger than any density-dependent condensates over the Borel window. This changes the conclusions about the density dependence of $m_ω$, indicating $\sim 40$ MeV increase at nuclear saturation density. △ Less

Submitted 7 August, 2000; v1 submitted 10 May, 2000; originally announced May 2000.

Comments: 8 pages, Revtex

Report number: UMN-TH-1903-00, TPI/MINN-00/22

Journal ref: Phys.Rev. C63 (2001) 015204

Generic and Cogeneric Monomial Ideals

Authors: Ezra Miller, Bernd Sturmfels, Kohji Yanagawa

Abstract: …their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley-Reisner complex. Reverse lexicographic initial ideals of generic la… ▽ More Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley-Reisner complex. Reverse lexicographic initial ideals of generic lattice ideals are generic. Cohen-Macaulayness for cogeneric ideals is characterized combinatorially; in the cogeneric case the Cohen-Macaulay type is greater than or equal to the number of irreducible components. Methods of proof include Alexander duality and Stanley's theory of local h-vectors. △ Less

Submitted 22 December, 1998; originally announced December 1998.

Comments: 15 pages, LaTeX

Report number: formerly math.AG/9812126 MSC Class: 13D02; 13H10; 13P10 (Primary); 52B20; 05E99 (Secondary)

Quark Propagator and Meson Correlators in the QCD Vacuum

Authors: Varun Sheel, Hiranmaya Mishra, Jitendra C. Parikh

Abstract: Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. Given such an ansatz we make no further approximations in the evaluation of the correlators. Our calculations for the… ▽ More Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. Given such an ansatz we make no further approximations in the evaluation of the correlators. Our calculations for the vector, axial vector and scalar channels show qualitative agreement with the phenomenological predictions, whereas the pseudoscalar channel does not. However, the pseudoscalar correlator, when approximated by saturating with intermediate one pion states agrees with results obtained from spectral density functions parameterised by pion decay constant and $<-\bar ψψ>$ value obtained from chiral perturbation theory. We discuss this departure in the pseudoscalar channel, in context of the quark propagation in the vacuum. △ Less

Submitted 11 July, 1997; originally announced July 1997.

Comments: 13 pages (including 3 figures), Latex, uses epsf style option and ijmpe1.sty file, submission in the form of uufile containing paper,3 figure ps files and ijmpe1.sty

Journal ref: Int.J.Mod.Phys. E6 (1997) 275-286

Meson Correlators in QCD Vacuum - is Saturation the Right Approach ?

Authors: Varun Sheel, Hiranmaya Mishra, Jitendra C. Parikh

Abstract: Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. With exact calculations,… ▽ More Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. With exact calculations, vector, axial vector and scalar channels show qualitative agreement with the phenomenological predictions, where as pseudoscalar channel does not. However, the pseudoscalar correlator, when approximated by saturating with intermediate one pion states agrees with results obtained from spectral density functions parametrised by pion decay constant and $<\bar ψψ>$ value obtained from chiral perturbation theory. △ Less

Submitted 24 November, 1994; originally announced November 1994.

Comments: 14 pages, REVTeX and EPSF file; 2 figures appended as a uuencoded compressed file (using uufiles)

Report number: PRL-TH/94-36