arXiv subjects

Amir Jafari

Publications and source records attributed to Amir Jafari.

At least 19 recordsLinked to original sources

arXiv2026

On union-closed families with prescribed number of $k$-sets

Fix positive integers $N,k,n$ with $n\ge k$. We seek the minimum number of members of size at least $n$ in a finite family of finite sets closed under union and containing exactly $N$ distinct sets of size $k$. This problem is a specialization of the Leck--Roberts--Simpson weighted conjecture: assign weight one to sets of size at least $n$ and zero to smaller sets. The predicted minimizer consists of the unions of nonempty subfamilies of the first $N$ $k$-subsets of the natural numbers, ordered by their largest elements and, when these agree, by their increasing lists lexicographically. For an integer $t\ge 1$, call the range \[ \binom{n+t-1}{k} \frac{5}{2} k^2t$. For sufficiently large $k$, we obtain a sufficient bound of order $k^2t/\log k$, uniformly in $t\ge2$.

math.CO↗

arXiv2026

Dynamic Alignment or Angular Persistence?

Dynamic alignment in magnetohydrodynamic turbulence is commonly inferred from the decrease of an amplitude-weighted average of the mutual angle between Els\"asser increments toward smaller separations. That decrease, however, need not imply that the increments themselves rotate toward alignment: large-angle fluctuations can simply lose more amplitude than small-angle ones. We therefore study the joint evolution of increment amplitude and mutual angle using finite-step conditional transition probabilities. In forced incompressible full MHD and in balanced strong-guide-field reduced MHD, we find that, at fixed initial angle, large-amplitude Els\"asser-increment pairs undergo smaller angular changes than small-amplitude pairs, including when they begin at large angles. We call this amplitude-dependent angular persistence. Independently, normalized amplitude moments increase toward smaller separation, while stronger amplitude weighting produces progressively smaller angular averages and stronger scale dependence, linking apparent alignment to the intermittent large-amplitude tail. In RMHD, a source-state decomposition of the Politano-Pouquet third-order moment shows that initially large-angle, high-amplitude populations contribute with the sign associated with transfer toward smaller perpendicular scales despite their comparatively small angular changes. Time-resolved full-MHD data reproduce the same amplitude ordering, and the local Els\"asser advective term closely tracks the conditional dependence of both angular and amplitude changes on the initial state. These results show that the conventional dynamic-alignment diagnostic reflects the joint statistical evolution of amplitude and angle and, by itself, is not evidence for a population-wide dynamical rotation toward alignment.

physics.plasm-ph↗

arXiv2026

The List Edge-Coloring Conjecture for Two New Infinite Families of Complete Graphs

Let $p$ be an odd prime. We prove the List Edge-Coloring Conjecture for two infinite families of complete graphs: \[ \chi'_{\ell}(K_{p-1})=p-2, \qquad \chi'_{\ell}(K_{2p})=2p-1. \] The two proofs control the Pfaffian sign of one-factorizations by complementary modular methods. For $K_{p-1}$, Frobenius and a skew specialization turn Glynn's determinant-coefficient congruence into a squarefree Pfaffian coefficient. A divided difference then reduces the remaining calculation to a single antidiagonal Pfaffian and gives \[[x^{\mathbf{1}}]\mbox{Pf}(X)^{p-2}\equiv(-2)^{(p-1)/2}\pmod{p}.\] For $K_{2p}$, a weighted Burnside count for the translation group $\Bbb{F}_p^2$ isolates a signed cyclic-starter sum. A skew-circulant cofactor identity evaluates its square and gives \[ S_{2p}\equiv-p\pmod{p^2}. \] In particular, both decisive signed sums are nonzero. Neither congruence is a formal consequence of Latin-square parity: the bipartite determinant sign and the nonbipartite Pfaffian sign are different invariants. Instead, the proofs develop a determinant--Pfaffian bridge and a signed Burnside--Fourier method adapted to the complete-graph sign. We also locate a limit of the latter method. For every even $b\ge4$, the signed trace of a full-support translation on $K_{bp}$ is divisible by $p^b$. For $b=4$ this implies $p^4\mid S_{4p}$ but supplies no nonzero residue, revealing a valuation barrier to the full-support higher-layer argument.

math.CO↗

arXiv2026

Frobenius-Power Ideals and Hyperplane Avoidance for Representable Matroids

Let $q=p^k$, where $p$ is prime, and let $M$ be a finite matroid representable over ${\Bbb{F}}_q$. Write $\chi_M(t)$ for its characteristic polynomial and $\mbox{decop}(M)$ for the least number of independent sets needed to cover its ground set. We prove that $\chi_M(q)>0$ whenever $k\ge\mbox{decop}(M)$. Geometrically, the central hyperplanes determined by any representation of $M$ fail to cover the dual of the ambient vector space. The proof rests on the Frobenius-power ideals $(X_1^{p^s},\ldots,X_n^{p^s})$, $s\ge1$. Each is preserved by every linear change of coordinates, while nonmembership records the existence of a monomial whose exponent in every variable is bounded. This permits successive normalizations of several invertible systems of linear forms without losing the exponent bounds already obtained. The coefficient form of the Combinatorial Nullstellensatz then produces a common nowhere-zero point. Finally, we test the scope of the theorem. M.~J.~Moghaddamzadeh's unpublished conjecture predicts a stronger statement over prime fields. Projective geometries show that its direct analogue fails over proper extension fields, even under the same numerical inequality.

math.CO↗

arXiv2026

Multi-Scale Coherence of Represented Flows

Many problems in nonlinear and statistical physics are formulated through represented flows, including physical-space vector fields, phase-space drift fields, and truncated renormalization-group beta functions. We introduce a complementary representation-dependent diagnostic for testing whether finite-separation flow geometry is stable across observational resolution. For two separated points, states, or theories, the method compares the direction of the corresponding vector-field increment after the field has been smoothed at two resolutions. Averaging this normalized comparison over sampled separations gives a coherence matrix tied to the chosen variables, coarse graining, metric, and sampling protocol; it is a consistency test, not a coordinate-invariant quantity. We demonstrate the diagnostic in three settings. Synthetic divergence-free fields with identical Fourier amplitudes, spectra, and scalar two-point correlations nevertheless produce distinct coherence matrices, showing that second-order statistics do not determine cross-resolution increment geometry. Lorenz phase-space tests show that a smooth coordinate wrinkling changes represented drift geometry without changing the underlying dynamics, and that a weak model perturbation lowers finite-separation coherence even when local stretching proxies remain closely matched. Finally, for functional renormalization-group flows of the three-dimensional $O(1)$ scalar theory, projected $M=4,5,6$ LPA beta fields remain internally coherent, while cross-truncation coherence decreases as higher-order coupling directions are activated. The diagnostic provides a practical field-level check of how representations, models, and truncations preserve finite-separation flow geometry, complementing rather than replacing standard local, spectral, or fixed-point diagnostics.

cond-mat.stat-mech↗

arXiv2026

Non-Dynamic Alignment in Magnetohydrodynamic Turbulence

Dynamic alignment in MHD turbulence is commonly interpreted as a tendency of Els\"asser increments to align toward smaller inertial-range scales. This interpretation is based on the amplitude-weighted diagnostic $\langle A_r\sin\theta_r\rangle/\langle A_r\rangle$, where $A_r$ is the product of the two increment amplitudes and $\theta_r$ is the unweighted folded angle. We show that a decrease of the weighted angle toward smaller scales does not require dynamical alignment but can arise from a retention effect in measurements. At fixed scale, larger amplitudes correlate with smaller angles, making the weighted angle smaller than the unweighted angle without implying that the angular population evolves toward alignment with scale. The same covariance-driven reweighting structure underlies the Price equation in evolutionary biology. Applied here in scale space, it separates angular evolution from redistribution of amplitude weight: a lower measured weighted angle at smaller scales can reflect reweighting even when the unweighted angle remains nearly scale independent. In physical time, the picture predicts that, after matching initial amplitudes, high-amplitude large-angle fluctuations lose a larger amplitude fraction over finite lags than high-amplitude small-angle fluctuations, favoring intense small-angle events in weighted statistics. This retention picture allows perpendicular rms Els\"asser increments to scale as $\ell_\perp^{1/4}$, corresponding to an effective $k_\perp^{-3/2}$ spectrum, without requiring dynamic alignment of typical fluctuations. We test these results using the Johns Hopkins Turbulence Database and NASA Wind measurements. Mean logarithmic increment amplitudes give steeper typical-amplitude slopes than rms-amplitude fits in both datasets, showing stronger sensitivity of second-order statistics to intermittent intense events.

physics.plasm-ph↗

arXiv2026

Statistical Flux Freezing with Magnetic Path-lines in Turbulence

Magnetic flux freezing states that, in ideal magnetohydrodynamics, magnetic flux is transported by the flow and magnetic field lines remain frozen into the plasma. In turbulent plasmas, however, the velocity and magnetic fields are spatially rough, invalidating the regularity assumptions underlying the classical theorem. Previous work has shown that Lagrangian trajectories in such rough flows can become nonunique in the limit of small magnetic diffusivity, leading to stochastic formulations of magnetic flux freezing based on magnetic field lines. Field lines, however, are instantaneous geometric objects that do not possess a natural time evolution and do not preserve identity in turbulent flows. We instead use magnetic path lines, which remain intrinsically stochastic in the ideal limit, implying that magnetic flux is conserved only in a statistical sense over ensembles of backward-advected path-line surfaces. This yields a statistical formulation of Alfven's theorem in terms of magnetic path lines and shows that the classical deterministic form of flux freezing cannot hold in sufficiently rough turbulent magnetic fields. While closely related in physical content to earlier stochastic flux-freezing approaches based on magnetic field lines, the path-line formulation provides time-evolving dynamical trajectories that retain identity in spacetime and offer a simpler and more transparent framework for analyzing stochastic magnetic transport.

physics.plasm-ph↗

arXiv2026

Noncommutative Wilczynski Invariants, and Modular Differential Equations

We develop a noncommutative invariant theory for ordinary linear differential operators on Riemann surfaces. For a monic binomially normalized operator $L=\sum_{k=0}^n {n\choose k}a_kD^{\,n-k}$, $a_0=1$, with coefficients in an associative differential algebra, we construct universal gauge-covariant coefficients $I_m(L)$. After correcting their reparametrization anomalies, we obtain Wilczy\'nski currents $W_m(L)$, which transform as genuine $m$-differentials. The construction is algebraic, finite-layered, and valid over noncommutative coefficient algebras; in the commutative scalar case it recovers the classical Wilczy\'nski invariants. We globalize the theory using jet bundles and infinitesimal neighborhoods of the diagonal. The natural global objects are $A$-linear opers, where $A$ is a sheaf of associative algebras with a compatible connection. In this setting $P=I_2/(n+1)$ is an $A_{\mathrm{ad}}$-valued projective connection, while $W_m$, $m\ge 3$, are global $A_{\mathrm{ad}}$-valued differentials; scalar invariants are obtained from traces, characteristic coefficients, and cyclic trace polynomials. As applications, we discuss projective connections, symmetric powers, fanning curves in Grassmannians, Calabi--Yau Picard--Fuchs equations, weak scalar and matrix-valued $W_2$-structures from Hodge subvariations, and modular differential equations. In the modular setting, the currents become modular forms, and the first coefficient gives the modular connection underlying the Serre derivative. We also extend the formalism to Siegel space using central Siegel modular connections and the associated equivariant differential algebra.

math.AG↗

arXiv2026

The Structure of Poloidal Fields Embedded in Thin Disks

Many accreting systems are modeled as geometrically thin disks. Simulations of accretion disks cannot be extended to this regime, although local models can address the behavior of narrow annuli. A global model needs to account for the interactions between a large-scale poloidal field, accreted from the environment, and the disk. The disk magnetosphere can be modeled subject to the boundary conditions imposed by the disk. These depend on the structure of the magnetic field as it crosses the disk and the degree to which the disk can support a bend in the field lines. Building on earlier work we derive a set of equations describing a stationary disk with an embedded poloidal field. We derive a modified induction equation that incorporates tensorial turbulent diffusivities and a helicity-regulated $\alpha$-effect. We quantify how helicity conservation introduces a nonlinear backreaction on the large-scale dynamo, dynamically coupling turbulent diffusion and $\alpha$-quenching. We discuss the challenges encountered in finding a unique solution under stationary flows $E_\phi =0$, which balances the inflow of $B_z$ due to accretion, the outflow due to radial diffusion of $B_z$, and the vertical movement of $B_r$ due to turbulent diffusion and buoyancy. The vertical profiles of both the azimuthal diffusion coefficient $D_{ijk}$ and the helicity-driven $\alpha_{ij}$ demonstrate that changes in the radial gradient can restructure the magnetic field geometry. The ability of disks to sustain large bending angles in the poloidal field implies that angular momentum flux through the magnetosphere can dominate over internal transport even for weak fields. Competing factors can result in non-unique solutions, necessitating extra constraints and diagnostics that highlight the role of isotropic turbulence and helicity regulation in magnetized disk environments.

astro-ph.HE↗

arXiv2025

Non-Gaussian statistics of concentration fluctuations in free liquid diffusion

We show that the three-point skewness of concentration fluctuations is non-vanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. We exploit a high-Schmidt reduction of nonlinear Landau-Lifshitz hydrodynamics for a binary fluid, both analytically and by a massively parallel Lagrangian Monte Carlo simulation. Non-Gaussian statistics result from nonlinear coupling of concentration fluctuations to thermal velocity fluctuations, analogous to the turbulent advection of a passive scalar. Concentration fluctuations obey no central limit theorem, counter to the predictions of macroscopic fluctuation theory for generic diffusive systems.

cond-mat.stat-mech↗

arXiv2025

Emergence of long-range non-equilibrium correlations in free liquid diffusion

It is experimentally well-established that non-equilibrium long-range correlations of concentration fluctuations appear in free diffusion of a solute in a solvent, but it remains unknown how such correlations are established dynamically. We address this problem in a model of Donev, Fai \& Vanden-Eijnden (DFV), obtained from the high-Schmidt limit of the Landau-Lifschitz fluctuating hydrodynamic equations for a binary mixture. We consider an initial planar interface of the mean concentration field in an infinite space domain, idealizing prior experiments. Using methods borrowed from turbulence theory, we show both analytically and numerically that a quasi-steady regime with self-similar time decay of concentration correlations appears at long time. In addition to the expected ``giant concentration fluctuations'' with correlations $\propto r$ for $r\lesssim L(t)=(Dt)^{1/2},$ with diffusivity $D,$ a new regime with spatial decay $\propto 1/r$ appears for $r\gtrsim L(t).$ The quasi-steady regime arises from an initial stage of transient growth $\propto t,$ confirming the prediction of DFV for $r\gtrsim L(t)$ and discovering an analogous result for $r\lesssim L(t).$ Our results give new insight into the emergence of non-equilibrium long-range correlations and provide novel predictions that may be investigated experimentally.

cond-mat.stat-mech↗

arXiv2025

Effective Field Theories in Magnetohydrodynamics

We briefly review the recent developments in magnetohydrodynamics, which in particular deal with the evolution of magnetic fields in turbulent plasmas. We especially emphasize (i) the necessity of renormalizing equations of motion in turbulence where velocity and magnetic fields become Hölder singular; (ii) the breakdown of Laplacian determinism (spontaneous stochasticity) for turbulent magnetic fields; and (iii) the possibility of eliminating the notion of magnetic field lines, using instead magnetic path lines as trajectories of Alfvenic wave-packets. These methodologies are then exemplified with their application to the problem of magnetic reconnection -- rapid change in magnetic field pattern that accelerates plasma -- a ubiquitous phenomenon in astrophysics and laboratory plasmas. The necessity of smoothing out rough velocity and magnetic fields on a finite scale L implies that magnetohydrodynamic equations should be regarded as effective field theories with running parameters depending upon the scale L.

physics.plasm-ph↗

arXiv2025

Does Magnetic Reconnection Change Topology?

We employ well-known concepts from statistical physics, quantum field theories and general topology to study magnetic reconnection, topology-change and their connection in incompressible flows in the context of an effective field theory without appealing to magnetic field lines. We consider the dynamical system corresponding to wave-packets moving with Alfven velocity dx/dt=V_A whose trajectories x(t) define path lines, which naturally provides a mathematical way to estimate the rate of magnetic topology-change. In laminar and even chaotic flows, the separation of path lines at all times remains proportional to their initial separation, argued to correspond to slow reconnection, and topology changes by dissipation with a rate proportional to resistivity. In turbulence, path lines diverge super-linearly with time independent of their initial separation, i.e., fast reconnection, and magnetic topology changes by turbulent dissipation with a rate independent of small-scale plasma effects. In fact, due to the loss of Lipschitz continuity of magnetic field in turbulence, path lines separate super-linearly even if their initial separation tends to vanish, unlike deterministic chaos. This super-chaotic behavior is an example of spontaneous stochasticity in statistical physics, sometimes called the real butterfly effect in chaos theory to distinguish it from the butterfly effect in which trajectories can diverge exponentially only if initial separation remains finite. If 3D reconnection is defined as magnetic topology-change, it can be fast only in turbulence where both reconnection and topology-change are driven by spontaneous stochasticity, independent of any plasma effects. Our results strongly support the Lazarian-Vishniac theory of turbulent reconnection.

physics.plasm-ph↗

arXiv2024

TVIM: Thermo-Active Variable Impedance Module: Evaluating Shear-Mode Capabilities of Polycaprolactone

In this work, we introduce an advanced thermo-active variable impedance module which builds upon our previous innovation in thermal-based impedance adjustment for actuation systems. Our initial design harnessed the temperature-responsive, viscoelastic properties of Polycaprolactone (PCL) to modulate stiffness and damping, facilitated by integrated flexible Peltier elements. While effective, the reliance on compressing and the inherent stress relaxation characteristics of PCL led to suboptimal response times in impedance adjustments. Addressing these limitations, the current iteration of our module pivots to a novel 'shear-mode' operation. By conducting comprehensive shear rheology analyses on PCL, we have identified a configuration that eliminates the viscoelastic delay, offering a faster response with improved heat transfer efficiency. A key advantage of our module lies in its scalability and elimination of additional mechanical actuators for impedance adjustment. The compactness and efficiency of thermal actuation through Peltier elements allow for significant downsizing, making these thermal, variable impedance modules exceptionally well-suited for applications where space constraints and actuator weight are critical considerations. This development represents a significant leap forward in the design of variable impedance actuators, offering a more versatile, responsive, and compact solution for a wide range of robotic and biomechanical applications.

cs.RO↗

arXiv2024

Agonist-Antagonist Pouch Motors: Bidirectional Soft Actuators Enhanced by Thermally Responsive Peltier Elements

In this study, we introduce a novel Mylar-based pouch motor design that leverages the reversible actuation capabilities of Peltier junctions to enable agonist-antagonist muscle mimicry in soft robotics. Addressing the limitations of traditional silicone-based materials, such as leakage and phase-change fluid degradation, our pouch motors filled with Novec 7000 provide a durable and leak-proof solution for geometric modeling. The integration of flexible Peltier junctions offers a significant advantage over conventional Joule heating methods by allowing active and reversible heating and cooling cycles. This innovation not only enhances the reliability and longevity of soft robotic applications but also broadens the scope of design possibilities, including the development of agonist-antagonist artificial muscles, grippers with can manipulate through flexion and extension, and an anchor-slip style simple crawler design. Our findings indicate that this approach could lead to more efficient, versatile, and durable robotic systems, marking a significant advancement in the field of soft robotics.

cs.RO↗

arXiv2023

Towards a Unified Naming Scheme for Thermo-Active Soft Actuators: A Review of Materials, Working Principles, and Applications

Soft robotics is a rapidly growing field that spans the fields of chemistry, materials science, and engineering. Due to the diverse background of the field, there have been contrasting naming schemes such as 'intelligent', 'smart' and 'adaptive' materials which add vagueness to the broad innovation among literature. Therefore, a clear, functional and descriptive naming scheme is proposed in which a previously vague name -- Soft Material for Soft Actuators -- can remain clear and concise -- Phase-Change Elastomers for Artificial Muscles. By synthesizing the working principle, material, and application into a naming scheme, the searchability of soft robotics can be enhanced and applied to other fields. The field of thermo-active soft actuators spans multiple domains and requires added clarity. Thermo-active actuators have potential for a variety of applications spanning virtual reality haptics to assistive devices. This review offers a comprehensive guide to selecting the type of thermo-active actuator when one has an application in mind. Additionally, it discusses future directions and improvements that are necessary for implementation.

cs.RO↗

arXiv2022

Comparison Study Between Token Classification and Sequence Classification In Text Classification

Unsupervised Machine Learning techniques have been applied to Natural Language Processing tasks and surpasses the benchmarks such as GLUE with great success. Building language models approach achieves good results in one language and it can be applied to multiple NLP task such as classification, summarization, generation and etc as an out of box model. Among all the of the classical approaches used in NLP, the masked language modeling is the most used. In general, the only requirement to build a language model is presence of the large corpus of textual data. Text classification engines uses a variety of models from classical and state of art transformer models to classify texts for in order to save costs. Sequence Classifiers are mostly used in the domain of text classification. However Token classifiers also are viable candidate models as well. Sequence Classifiers and Token Classifier both tend to improve the classification predictions due to the capturing the context information differently. This work aims to compare the performance of Sequence Classifier and Token Classifiers and evaluate each model on the same set of data. In this work, we are using a pre-trained model as the base model and Token Classifier and Sequence Classier heads results of these two scoring paradigms with be compared..

cs.CL↗

arXiv2022

A Deep Learning Anomaly Detection Method in Textual Data

In this article, we propose using deep learning and transformer architectures combined with classical machine learning algorithms to detect and identify text anomalies in texts. Deep learning model provides a very crucial context information about the textual data which all textual context are converted to a numerical representation. We used multiple machine learning methods such as Sentence Transformers, Auto Encoders, Logistic Regression and Distance calculation methods to predict anomalies. The method are tested on the texts data and we used syntactic data from different source injected into the original text as anomalies or use them as target. Different methods and algorithm are explained in the field of outlier detection and the results of the best technique is presented. These results suggest that our algorithm could potentially reduce false positive rates compared with other anomaly detection methods that we are testing.

cs.CL↗