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Dmitry Sokolov

Publications and source records attributed to Dmitry Sokolov.

At least 19 recordsLinked to original sources
arXiv2025

Sampling Permutations with Cell Probes is Hard

Suppose we are given an infinite sequence of input cells, each initialized with a uniform random symbol from $[n]$. How hard is it to output a sequence in $[n]^n$ that is close to a uniform random permutation? Viola (SICOMP 2020) conjectured that if each output cell is computed by making $d$ probes to input cells, then $d\geq\omega(1)$. Our main result shows that, in fact, $d\geq (\log n)^{\Omega(1)}$, which is tight up to the constant in the exponent. Our techniques also show that if the probes are nonadaptive, then $d\geq n^{\Omega(1)}$, which is an exponential improvement over the previous nonadaptive lower bound due to Yu and Zhan (ITCS 2024). Our results also imply lower bounds against succinct data structures for storing permutations.

cs.CC↗
arXiv2025

Monotone Circuit Complexity of Matching

We show that the perfect matching function on $n$-vertex graphs requires monotone circuits of size $\smash{2^{n^{Ω(1)}}}$. This improves on the $n^{Ω(\log n)}$ lower bound of Razborov (1985). Our proof uses the standard approximation method together with a new sunflower lemma for matchings.

cs.CC↗
arXiv2025

Pseudodeterministic Communication Complexity

We exhibit an $n$-bit partial function with randomized communication complexity $O(\log n)$ but such that any completion of this function into a total one requires randomized communication complexity $n^{\Omega(1)}$. In particular, this shows an exponential separation between randomized and \emph{pseudodeterministic} communication protocols. Previously, Gavinsky (2025) showed an analogous separation in the weaker model of parity decision trees. We use lifting techniques to extend his proof idea to communication complexity.

cs.CC↗
arXiv2025

Sign-Rank of $k$-Hamming Distance is Constant

We prove that the sign-rank of the $k$-Hamming Distance matrix on $n$ bits is $2^{O(k)}$, independent of the number of bits $n$. This strongly refutes the conjecture of Hatami, Hatami, Pires, Tao, and Zhao (RANDOM 2022), and Hatami, Hosseini, and Meng (STOC 2023), repeated in several other papers, that the sign-rank should depend on $n$. This conjecture would have qualitatively separated margin from sign-rank (or, equivalently, bounded-error from unbounded-error randomized communication). In fact, our technique gives constant sign-rank upper bounds for all matrices which reduce to $k$-Hamming Distance, as well as large-margin matrices recently shown to be irreducible to $k$-Hamming Distance.

cs.CC↗
arXiv2025

Exponential Resolution Lower Bounds for Weak Pigeonhole Principle and Perfect Matching Formulas over Sparse Graphs

We show exponential lower bounds on resolution proof length for pigeonhole principle (PHP) formulas and perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge to establish strong lower bounds in the regime between balanced constant-degree expanders as in [Ben-Sasson and Wigderson '01] and highly unbalanced, dense graphs as in [Raz '04] and [Razborov '03, '04]. We obtain our results by revisiting Razborov's pseudo-width method for PHP formulas over dense graphs and extending it to sparse graphs. This further demonstrates the power of the pseudo-width method, and we believe it could potentially be useful for attacking also other longstanding open problems for resolution and other proof systems.

cs.CC↗
arXiv2024

Supercritical Tradeoffs for Monotone Circuits

We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size-depth tradeoff result for monotone circuits in the so-called supercritical regime. Our proof is based on an analogous result in proof complexity: We introduce a new family of unsatisfiable 3-CNF formulas (called bracket formulas) that admit resolution refutations of quasipolynomial size while any refutation of polynomial depth requires exponential size.

cs.CC↗
arXiv2024

Top-Down Lower Bounds for Depth-Four Circuits

We present a top-down lower-bound method for depth-$4$ boolean circuits. In particular, we give a new proof of the well-known result that the parity function requires depth-$4$ circuits of size exponential in $n^{1/3}$. Our proof is an application of robust sunflowers and block unpredictability.

cs.CC↗
arXiv2024

Controllable suppression of the unconventional superconductivity in bulk and thin-film Sr$_{2}$RuO$_{4}$ via high-energy electron irradiation

In bulk Sr$_{2}$RuO$_{4}$, the strong sensitivity of the superconducting transition temperature $T_{\text{c}}$ to nonmagnetic impurities provides robust evidence for a superconducting order parameter that changes sign around the Fermi surface. In superconducting epitaxial thin-film Sr$_{2}$RuO$_{4}$, the relationship between $T_{\text{c}}$ and the residual resistivity $ρ_0$, which in bulk samples is taken to be a proxy for the low-temperature elastic scattering rate, is far less clear. Using high-energy electron irradiation to controllably introduce point disorder into bulk single-crystal and thin-film Sr$_{2}$RuO$_{4}$, we show that $T_{\text{c}}$ is suppressed in both systems at nearly identical rates. This suggests that part of $ρ_0$ in films comes from defects that do not contribute to superconducting pairbreaking, and establishes a quantitative link between the superconductivity of bulk and thin-film samples.

cond-mat.supr-con↗
arXiv2023

Sampling and Certifying Symmetric Functions

A circuit $\mathcal{C}$ samples a distribution $\mathbf{X}$ with an error $ε$ if the statistical distance between the output of $\mathcal{C}$ on the uniform input and $\mathbf{X}$ is $ε$. We study the hardness of sampling a uniform distribution over the set of $n$-bit strings of Hamming weight $k$ denoted by $\mathbf{U}^n_k$ for _decision forests_, i.e. every output bit is computed as a decision tree of the inputs. For every $k$ there is an $O(\log n)$-depth decision forest sampling $\mathbf{U}^n_k$ with an inverse-polynomial error [Viola 2012, Czumaj 2015]. We show that for every $ε> 0$ there exists $τ$ such that for decision depth $τ\log (n/k) / \log \log (n/k)$, the error for sampling $\mathbf{U}_k^n$ is at least $1-ε$. Our result is based on the recent robust sunflower lemma [Alweiss, Lovett, Wu, Zhang 2021, Rao 2019]. Our second result is about matching a set of $n$-bit strings with the image of a $d$-_local_ circuit, i.e. such that each output bit depends on at most $d$ input bits. We study the set of all $n$-bit strings whose Hamming weight is at least $n/2$. We improve the previously known locality lower bound from $Ω(\log^* n)$ [Beyersdorff, Datta, Krebs, Mahajan, Scharfenberger-Fabian, Sreenivasaiah, Thomas and Vollmer, 2013] to $Ω(\sqrt{\log n})$, leaving only a quartic gap from the best upper bound of $O(\log^2 n)$.

cs.CC↗
arXiv2023

Probing momentum-dependent scattering in uniaxially stressed Sr$_2$RuO$_4$ through the Hall effect

Under in-plane uniaxial stress, the largest Fermi surface sheet of the correlated metal Sr$_2$RuO$_4$ undergoes a Lifshitz transition from an electron-like to an open geometry. We investigate the effects of this transition on transport through measurement of the longitudinal resistivity $ρ_{xx}$ and the Hall coefficient $R_\text{H}$. At temperatures where scattering is dominated by electron-electron scattering, $R_\text{H}$ becomes more negative across the Lifshitz transition, opposite to expectations from the change in Fermi surface topology. We show that this change in $R_\text{H}$ is explainable only if scattering changes throughout the Brillouin zone, not just at the point in $k$-space where the Lifshitz transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with $xy$ orbital weight decreases dramatically. On the other hand, at temperatures where defect scattering dominates $ρ_{xx}$ and $R_\text{H}$ are essentially constant across the Lifshitz transition.

cond-mat.str-el↗
arXiv2022

Tuning the Fermi Liquid Crossover in Sr$_2$RuO$_4$ with Uniaxial Stress

We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr$_2$RuO$_4$, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasi-particle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi liquid coherence scale is shown to be tunable by strain, and driven to low values as the associated Lifshitz transition is approached.

cond-mat.str-el↗
arXiv2022

Practical lowest distortion mapping

Construction of optimal deformations is one of the long standing problems of computational mathematics. We consider the problem of computing quasi-isometric deformations with minimal possible quasi-isometry constant (global estimate for relative length change).We build our technique upon [Garanzha et al. 2021a], a recently proposed numerical optimization scheme that provably untangles 2D and 3D meshes with inverted elements by partially solving a finite number of minimization problems. In this paper we show the similarity between continuation problems for mesh untangling and for attaining prescribed deformation quality threshold. Both problems can be solved by a finite number of partial solutions of optimization problems which are based on finite element approximations of parameter-dependent hyperelastic functionals. Our method is based on a polyconvex functional which admits a well-posed variational problem. To sum up, we reliably build 2D and 3D mesh deformations with smallest known distortion estimates (quasi-isometry constants) as well as stable quasi conformal parameterizations for very stiff problems.

cs.CG↗
arXiv2021

Foldover-free maps in 50 lines of code

Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D space) is the most fundamental problem in geometry processing.In computational physics, untangling plays an important role in mesh generation: it takes a mesh as an input, and moves the vertices to get rid of foldovers.In fact, mesh untangling can be considered as a special case of mapping where the geometry of the object is to be defined in the map space and the geometric domain is not explicit, supposing that each element is regular.In this paper, we propose a mapping method inspired by the untangling problem and compare its performance to the state of the art.The main advantage of our method is that the untangling aims at producing locally injective maps, which is the major challenge of mapping.In practice, our method produces locally injective maps in very difficult settings, and with less distortion than the previous work, both in 2D and 3D. We demonstrate it on a large reference database as well as on more difficult stress tests.For a better reproducibility, we publish the code in Python for a basic evaluation, and in C++ for more advanced applications.

cs.CG↗
arXiv2019

Magnetic frustration and spontaneous rotational symmetry breaking in PdCrO2

In the triangular layered magnet PdCrO2 the intralayer magnetic interactions are strong, however the lattice structure frustrates interlayer interactions. In spite of this, long-range, 120$^\circ$ antiferromagnetic order condenses at $T_N = 38$~K. We show here through neutron scattering measurements under in-plane uniaxial stress and in-plane magnetic field that this occurs through a spontaneous lifting of the three-fold rotational symmetry of the nonmagnetic lattice, which relieves the interlayer frustration. We also show through resistivity measurements that uniaxial stress can suppress thermal magnetic disorder within the antiferromagnetic phase.

cond-mat.str-el↗
arXiv2017

Anti-aliasing for fused filament deposition

Layered manufacturing inherently suffers from staircase defects along surfaces that are gently slopped with respect to the build direction. Reducing the slice thickness improves the situation but never resolves it completely as flat layers remain a poor approximation of the true surface in these regions. In addition, reducing the slice thickness largely increases the print time. In this work we focus on a simple yet effective technique to improve the print accuracy for layered manufacturing by filament deposition. Our method works with standard three-axis 3D filament printers (e.g. the typical, widely available 3D printers), using standard extrusion nozzles. It better reproduces the geometry of sloped surfaces without increasing the print time. Our key idea is to perform a local anti-aliasing, working at a sub-layer accuracy to produce slightly curved deposition paths and reduce approximation errors. This is inspired by Computer Graphics anti-aliasing techniques which consider sub-pixel precision to treat aliasing effects. We show that the necessary deviation in height compared to standard slicing is bounded by half the layer thickness. Therefore, the height changes remain small and plastic deposition remains reliable. We further split and order paths to minimize defects due to the extruder nozzle shape, avoiding any change to the existing hardware. We apply and analyze our approach on 3D printed examples, showing that our technique greatly improves surface accuracy and silhouette quality while keeping the print time nearly identical.

cs.GR↗
arXiv2016

Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP

Weyl semimetals (WSMs) are topological quantum states wherein the electronic bands linearly disperse around pairs of nodes, the Weyl points, of fixed (left or right) chirality. The recent discovery of WSM materials triggered an experimental search for the exotic quantum phenomenon known as the chiral anomaly. Via the chiral anomaly nonorthogonal electric and magnetic fields induce a chiral density imbalance that results in an unconventional negative longitudinal magnetoresistance, the chiral magnetic effect. Recent theoretical work suggests that this effect does not require well-defined Weyl nodes. Experimentally however, it remains an open question to what extent it survives when chirality is not well-defined, for example when the Fermi energy is far away from the Weyl points. Here, we establish the detailed Fermi surface topology of the recently identified WSM TaP via a combination of angle-resolved quantum oscillation spectra and band structure calculations. The Fermi surface forms spin-polarized banana-shaped electron and hole pockets attached to pairs of Weyl points. Although the chiral anomaly is therefore ill-defined, we observe a large negative magnetoresistance (NMR) appearing for collinear magnetic and electric fields as observed in other WSMs. In addition, we show experimental signatures indicating that such longitudinal magnetoresistance measurements can be affected by an inhomogeneous current distribution inside the sample in a magnetic field. Our results provide a clear framework how to detect the chiral magnetic effect.

cond-mat.mtrl-sci↗
arXiv2015

Inappropriate use of L-BFGS, Illustrated on frame field design

L-BFGS is a hill climbing method that is guarantied to converge only for convex problems. In computer graphics, it is often used as a black box solver for a more general class of non linear problems, including problems having many local minima. Some works obtain very nice results by solving such difficult problems with L-BFGS. Surprisingly, the method is able to escape local minima: our interpretation is that the approximation of the Hessian is smoother than the real Hessian, making it possible to evade the local minima. We analyse the behavior of L-BFGS on the design of 2D frame fields. It involves an energy function that is infinitly continuous, strongly non linear and having many local minima. Moreover, the local minima have a clear visual interpretation: they corresponds to differents frame field topologies. We observe that the performances of LBFGS are almost unpredictables: they are very competitive when the field is sampled on the primal graph, but really poor when they are sampled on the dual graph.

cs.GR↗