A Heron triangle is a triangle whose side lengths and area are all positive integers. If the greatest common divisor of the three side lengths is $1$, it is called a primitive Heron triangle. In this paper, we give an equivalent condition for Heron triangles with all three sides being perfect squares, which reduces to finding non-trivial rational points on a family of algebraic curves of genus $3$. This leads us to believe that only finitely many Heron triangles with three perfect square sides exist. Using a specific elliptic curve, we completely characterize all Heron triangles with two sides that are perfect squares, and obtain a family of parametric solutions that yield primitive Heron triangles. This implies that there are infinitely many primitive Heron triangles having two sides as perfect squares.

Nitride perovskites are an emerging class of materials predicted to exhibit diverse functional properties, yet remain underexplored due to synthesis challenges of oxygen-free nitrides. Recently, LaMoN$_3$ has been reported as an oxygen-free nitride perovskite with polar symmetry, exhibiting excellent dynamic stability and ferroelectric properties under moderate pressure. However, its phase stability, linear and non-linear optical response, excitonic and polaronic behavior, and efficiency under high pressure remain unexplored. Applying pressure enables systematic tuning of the electronic structure properties, thereby facilitating the identification of phases optimized for either linear or nonlinear optical responses. Therefore, in this work, we systematically investigate these properties of LaMoN$_3$ up to 40 GPa using first-principles methods, including density functional theory, density functional perturbation theory, many-body perturbation theory (namely G$_0$W$_0$ and BSE), and tight binding approximation model. Our study shows that LaMoN$_3$ remains dynamically stable and retains its single-phase structure up to 40 GPa. The compound exhibits an indirect bandgap that decreases from 2.17 eV (0 GPa) to 1.45 eV (40 GPa) at the G$_0$W$_0$@PBE level. Using the BSE, we find that pressure enhances the SLME while lowering the exciton binding energy, both favorable for photovoltaic applications. The bulk photovoltaic efficiency trend with pressure mimics the behavior of the shift current density J$_SC$ , peaking near 15 GPa before declining at higher pressures due to a diminished nonlinear shift current response. These results highlight pressure-tuned regimes to enhance photovoltaic performance. We thereby propose multi-junction device, combining absorber layers optimized for linear and nonlinear optical currents, together boosting solar energy conversion through complementary mechanisms.

Modulation doping, a well-established technique for traditional semiconductor heterostructures, is a promising approach for tailoring carrier concentration in 2D materials devices. In this letter we report on photoinduced modulation doping in hBN-graphene-hBN-SiO2 heterostructures utilizing standard white light sources and no additional fabrication complexity. We establish the use of this technique to both dope the channel material and to photoanneal devices, providing control over electronic doping and disorder in the graphene channel. We analyze the transport properties by employing Drude and Landauer transport models, highlighting the ability to reversibly tune the mobility and mean scattering length of the graphene with a high degree of accuracy. This tunability allows us to switch our device between the diffusive and quasi-ballistic transport regimes in situ. We utilize the exceptional control our technique provides over local disorder to realize quantum Hall isospin ferromagnetic states in a device whose initial quality would otherwise leave such states unobservable. These results demonstrate precise manipulation of carrier density and charge disorder in van der Waals heterostructures, providing a highly accessible approach to creating high-quality devices capable of realizing correlated electronic states.

An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Since there is no effective formula to compute the distance of a point and a set, it is hard to determine the points of an equidistant set in general. Therefore, it is important to investigate some special cases. In the paper we investigate equidistant sets that can be given as the graph of a function. They are called equidistant functions. In the previously examined conceptual model, one of the focal sets is the horizontal hyperplane through the origin and the other one is the epigraph of a positive-valued, continuous function. The equidistant points form the graph of another function over the hyperplane. In a general situation, the hyperplane is the first-order (linear) approximation for one of the focal sets. A natural idea is to substitute the hyperplane by a circle (sphere) as a second-order (quadratic) approximation for one of the focal sets in more complicated cases. Such a generalization results in a new type of equidistant functions we are going to investigate in the present paper. Before considering the special cases in detail, we present some general observations: a necessary and sufficient condition for the existence of equidistant points along the vertical lines, upper/lower equidistant functions, equidistant functions, a necessary and sufficient condition for the existence of the equidistant function, equidistant functions and the minimum operator (a kind of commuting property).

A variant of the Falconer distance problem asks for fixed $k\geq 1$ and $d\geq k+1$, how large does the Hausdorff dimension of a Borel set $E\subset\mathbb{R}^d$ need to be to guarantee that there exist $x_0,\ldots,x_{k}\in E$ such that $\text{Vol}_{k+1}^{(x_0,\ldots,x_{k})}(E) = \lbrace \text{Vol}_{k+1}(x_0,\ldots,x_{k},x_{k+1}) : x_{k+1}\in E \rbrace$ has positive Lebesgue measure. Here $\text{Vol}_{k+1}(x_0,\ldots,x_{k},x_{k+1})$ denotes the $k+1$-volume of the $k+1$ simplex formed by $x_0,\ldots,x_{k},x_{k+1}$. Recently, Shmerkin and Yavicoli established a sharp dimensional threshold $k$ in the case when $d=k+1$. In this paper we extend their result to $k+1 \leq d \leq 2k$ and obtain a non-trivial dimensional threshold $d-k$ when $d>2k$. The result is motivated by ideas from Shmerkin and Yavicoli. A crucial part of the argument is an application of work by Bright, Ortiz and Zakharov on a continuum Beck-type theorem for hyperplanes as well as classic results of Marstrand on projections and slicing theorems. In addition, we investigate a more elementary approach under a condition called the Fubini property for Hausdorff dimension as introduced in the work of Héra, Keleti and Máthé.

Classical entropy regularization is poorly suited to continuous-time martingale transport, since relative entropy between diffusion laws typically forces their volatility characteristics to coincide. We introduce a specific-entropy framework based on Poisson jump approximations of continuous martingales. In the Gaussian-mark case, this yields explicit generalized specific entropy functionals on Wiener space, whose limiting costs depend not only on the limiting martingale laws but also on the microscopic approximation mechanism. This Poissonization approach avoids deterministic grid refinement and the associated high-dimensional multimarginal Sinkhorn problems, while allowing jump intensities to reflect local volatility. We prove weak convergence of the Poisson approximations and identify the limiting entropy functionals. For a trace-normalized Poisson scheme, the resulting cost defines a continuous-time specific-entropic martingale optimal transport problem, called SEMOT. This cost yields compactness, existence, and strong duality, and leads formally to a coupled Hamilton-Jacobi-Bellman/Fokker-Planck system. The resulting structure suggests Sinkhorn type numerical schemes, which we implement in one and two dimensions.

This work develops a framework to apply normalizing-flow transformations of field configurations for all-orders Quantum Electrodynamics (QED) corrections in lattice field theory. This opens a new possibility to determine all-order corrections without the need for additional Monte Carlo sampling, generally bypassing the complexity in Wick-contraction diagrams needed at fixed order. The new method is applied to lattice scalar QED in two, three, and four spacetime dimensions, using both analytical and machine-learned flows, with both approaches yielding estimates with significantly reduced variance with respect to standard methods. It is further shown that flows can be trained using small lattice geometries and subsequently evaluated on much larger lattice geometries while maintaining good efficiency. A generalization to theories with fermions is envisaged, suggesting a path to applications in challenging field theories including lattice Quantum Chromodynamics.

A detailed formulation of the relativistic plane-wave Born approximation for inelastic collisions of charged particles with free atoms and positive ions is presented. The wave functions of the target atom or ion are calculated from a central-field independent-electron model with the Dirac-Hartree-Fock-Slater self-consistent potential, and the electromagnetic field is expressed in the Coulomb gauge. The double-differential cross section, depending on the energy loss and the recoil energy, is given as a sum of two terms which are products of purely kinematic factors and the generalized oscillator strengths (GOSs). Transitions induced by the instantaneous Coulomb interaction between the projectile and the active target electron are described by the longitudinal GOS. Transitions caused by the transverse interaction (exchange of virtual photons) are accounted for by a transverse GOS. We derive closed expressions for the longitudinal and transverse GOSs in terms of vector coupling coefficients and radial integrals. A set of Fortran programs have been written to compute the GOSs, the energy-loss differential cross section, and integrals of the latter. A complete numerical database of GOSs has been calculated for all the subshells of the ground-state configuration of neutral atoms of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). A systematic derivation of asymptotic formulas for the total cross section, the stopping cross section and the energy-straggling cross section is presented. The shell correction to the asymptotic formula for the stopping cross section of protons is obtained from the difference between computed numerical values and the predictions of that formula.

We establish the foundations of categorical weave calculus, developing the diagrammatic calculus of weaves and braid varieties within the study of Calabi-Yau triangulated categories and cluster tilting theory. This is achieved by associating a perverse sheaf of triangulated categories to each Demazure weave. A central contribution is the construction and study of the categorical Lusztig cycles and their duals, which we show form simple-minded and silting collections in the category of global sections of such a sheaf of categories. These categorical collections are built using the diagrammatics of weaves and we study their behavior under changes of weaves. For instance, we show that they undergo tilts under weave mutations. En route, we develop the study of categorical weighted braid words, as canonical rigid filtered dg modules over derived preprojective algebras, and the categorical incarnation of the tropical Lusztig rules, as a gluing mechanism for such filtered objects. Appendix A contains homological results, providing a novel construction of simple-minded and silting collections from full exceptional collections, and characterizing when these arise from a highest weight structure on an abelian category.

We study permutation-invariant quantum codes in the symmetric subspace $\mathrm{Sym}^n(\mathbb{C}^q) $ of $n$ qudits of local dimension $q$. For every integer $q\geq 2$, we construct a permutation-invariant code with parameters $((4,q,2))_q$. Thus four physical qudits suffice to encode one logical qudit with distance two in the symmetric sector for every local dimension. We also show, using linear-programming constraints for permutation-invariant quantum codes, that no permutation-invariant code of dimension $q$ and distance at least $2$ exists in $\mathrm{Sym}^n(\mathbb{C}^q)$ for $n\leq 3$. Hence four qudits are necessary and sufficient. The construction has a simple representation-theoretic and combinatorial description. In the irreducible $\mathrm{SU}(q)$-module $\mathrm{Sym}^4(\mathbb{C}^q)$, the distance-two Knill-Laflamme conditions split into root and Cartan parts. By restricting supports to the even-entry occupation layer, all root-error conditions vanish automatically. The remaining Cartan conditions reduce to linear balancing constraints on packets of occupation vectors. These packets admit a natural graph-theoretic interpretation in terms of the vertices and edges of the complete graph $K_q$: for odd $q$, they are organized by the midpoint rule, while for even $q$, they are organized by a decomposition of $K_q$ into perfect matchings. In this way, the existence of minimal $((4,q,2))_q$ permutation-invariant codes is reduced to a parity-dependent edge-coloring problem on $K_q$.

We study the Lorentzian Wetterich Renormalization Group (RG) flow equation for interacting quantum fields on curved backgrounds within the framework of perturbative Algebraic Quantum Field Theory (pAQFT). Specifically, we consider two classes of models: two mutually interacting scalar fields on globally hyperbolic spacetimes without boundary and, under the further assumption that the underlying background is spin, self-interacting Dirac fields. In both cases, we derive the corresponding RG flow equations within a Local Potential Approximation and compute the beta functions for the relevant couplings. For the scalar model, we also discuss an asymmetric interaction potential which is formally reminiscent of the Martin-Siggia-Rose description of a stochastic dynamics, thereby indicating a possible connection between Lorentzian algebraic RG methods [DDP+24] and stochastic field-theoretic models, [Duc25]. In addition, we address the local well-posedness of the resulting flow equations. Adapting the strategy detailed in [DP23] and based on the the Nash-Moser theorem, we prove local existence and uniqueness of solutions for both the scalar and the Dirac models.

Building on Padmanabhan's entropy functional, originally introduced to derive Einstein's equations and highlight the emergent nature of gravity, we demonstrate its robustness in a broader context. Using the same entropy density, we show that the Brown-York (BY) tensor arises naturally as the projection of the canonical momentum conjugate to the normal vectors on the relevant hypersurface, thereby providing a common construction applicable to both timelike and null hypersurfaces. This perspective also offers insight into the structural differences of the null BY tensor, including its non-symmetric character. We further extend the analysis to scalar-tensor theories, showing that the entropy-based formulation reproduces the expected equations of motion along with the corresponding BY tensor, and, clarifies its non-conservation in the presence of additional scalar field which is non-minimally coupled. Our results provide a coherent variational interpretation of quasi-local gravitational quantities and reveal a common underlying structure linking bulk dynamics and boundary momentum.

As trapped-ion quantum computing scales to larger qubit registers and more complex control protocols, classical control systems face a fundamental tradeoff: sub-microsecond board-level feedback requires tight hardware coupling, whereas maintainability and extensibility require clean, modular software abstractions. This paper presents QuCtrl-BELL (Bell), a compiler-driven software stack for trapped-ion quantum control. The design resolves this tradeoff by decoupling control flow -- including loops, branches, and synchronization -- from hardware state data. A Python-embedded domain-specific language (DSL) is lowered through a six-stage transpilation pipeline covering control flow graph (CFG) construction, static single-assignment (SSA) conversion, liveness analysis, and graph-coloring register allocation. The compiler generates deterministic distributed board-level programs and compact step-table data. A cross-board synchronization protocol supports feedback loops with latency below 700~ns without host intervention. Bell is deployed and evaluated on the QuCtrl-BELL platform (RISC-V + PXIe), demonstrating that a compiler-based infrastructure can provide programmability, deterministic timing, and modularity for scalable trapped-ion quantum control.

Given a minimal action $G\curvearrowright X$ of a countable group $G$ on a compact space $X$, we prove that if the reduced crossed product $G\ltimes_rC(X)$ is simple, then there exists a point whose stabilizer subgroup has trivial amenable radical. As a consequence, we give a complete characterization of the simplicity of the reduced crossed product of minimal actions of countable linear groups, hyperbolic groups, and, more generally, for groups with countably many amenable subgroups. This answers a question of Ozawa (2014) for these classes of groups. Furthermore, in the case of an infinite uniformly recurrent subgroup of a $C^*$-simple group, we prove that almost every subgroup has a trivial amenable radical, with respect to a fully supported, atomless probability measure.

Reducing collective communication latency is a critical goal for large model training and inference in both academia and industry. Many-to-many communications, such as AllGather and AlltoAll (dispatch), are core components of modern parallelization strategies. State-of-the-art implementations of these communications rely on unicast-based writes and transmit duplicate copies of the same data across physical links for multiple receivers. This redundant transmission congests network bottlenecks and degrades end-to-end latency. We present MultiWrite, a novel many-to-many transmission semantic that eliminates redundant packets to directly reduce operator latency. MultiWrite adopts multicast principles while addressing critical limitations of traditional multicast for AI workloads. These limitations include heavy management plane overhead and ecosystem compatibility issues. We implement MultiWrite on Ascend NPUs. Long-term stress tests demonstrate that our MultiWrite-based operators achieve up to 33% latency reduction on commercially deployed devices.

Erasure codes are a critical component in reliable storage systems today, and many blockchain systems use consensus protocols that involve erasure codes to reduce their communication cost. Existing erasure codes rely on a threshold failure assumption, but recent blockchain systems have departed from this simple model and use generalized failure assumptions. This paper introduces monotone erasure codes that respect arbitrary trust assumptions on a set of nodes. The paper first describes a method for constructing a monotone erasure code from any access structure given by a monotone Boolean formula. Next, the relevant notion of a linear monotone erasure code is introduced, which works on vectors over a finite field and where the encoding is a linear operation. We then focus on constructing linear monotone erasure codes: We give an efficient algorithm to construct linear monotone erasure codes for any access structure, and we show how to efficiently construct linear monotone erasure codes for the special case of partitioned access structures with minimal storage overhead. Last but not least, this work also shows how to use monotone erasure codes to obtain a communication-efficient, generalized version of the well-known asynchronous verifiable information dispersal (AVID) primitive, which is a key building block for developing efficient reliable broadcast and consensus protocols.

The evaluation of the Riemann zeta function at negative integers is a classical result typically obtained through analytic continuation or contour integration. In this paper, we present a novel and concise derivation of these special values by employing the theory of Cesàro limit of distributions, a generalized limit concept developed by Estrada, Kanwal, and Fulling. We use this tool to give a quick proof of the result that \[ ζ(-n)=-\frac{B_{n+1}}{n+1}, \] for $n\in\mathbb{N}^+.$ We also give a short discussion on $ζ^{\prime }(α)$ and compute the value of $ζ^{\prime}(0)$.

We introduce a new method for computing plus-pure thresholds, a mixed-characteristic analogue of both log canonical thresholds and $F$-pure thresholds. We obtain some necessary conditions and some sufficient conditions for BCM-regularity of Fermat-type hypersurfaces. We also establish lower bounds for plus-pure thresholds of diagonal hypersurfaces in mixed characteristic. Furthermore, we give bounds for plus-pure thresholds of hypersurfaces in mixed characteristic $(0,2)$ using splitting-order sequences, introduced by Yoshikawa. As an application, we classify BCM-regular diagonal hypersurfaces in mixed characteristic $(0,2)$.

We introduce a functor from cochain complexes to bicomplexes, called inflation functor, which sends quasi-isomorphisms to the class of pluripotential weak equivalences. We show this functor is part of a Quillen adjunction. Its right adjoint is a well-known construction in complex geometry, which gives a sheaf-theoretic presentation of Bott-Chern and Aeppli cohomologies. The inflation functor plays a key role in pluripotential Koszul duality theory for operads and allows us to construct the infinity-category of bicomplexes in the pluripotential sense.

Transition metal oxide perovskites are an ideal platform for exploring the interplay between spin, orbital, charge and lattice degrees of freedom. Among them, \ce{LaVO3} has been extensively studied in heterostructures and superlattices, where exotic phases have been reported. Motivated by the advances in freestanding oxide membranes, we investigate the intrinsic properties of freestanding ultrathin \ce{LaVO3} films using density functional theory. Our calculations reveal a sequence of magnetic phase transitions with thickness, starting from stripe-AFM in monolayer until the bulk like C-AFM is recovered. Beyond four layers, polar catastrophe driven charge transfer dopes the surface layers giving rise to stripe-AFM and ferromagnetic surface states while the central layers remain bulk like. We further explore this fact by studying charge doped monolayer, discovering that hole doping drives the system into ferromagnetic state. Doping also induced charge ordering in the system. A striped charge ordering pattern is observed at 0.5 h/fu, while a 3:1 stripe pattern emerges at 0.25 h/fu, indicating that the periodicity of the superstructure changes with doping concentration.

This Letter discusses two retrodictions of the law of ratchet universality which explain previous numerical and experimental results concerning the diode effect in conventional superconducting tunnel-junctions in one case, and controlled suppression of electron-hole pair generation in a tunnel junction in the other, both in the presence of biharmonic driving fields. Our study demonstrates that the ratchet universal driving field maximizes the diode's efficiency while yielding a maximal rectification range for the supercurrent, on the one hand, and optimally reduces the excess quantum noise with respect to the dc noise level, thus allowing for the efficient production of nonclassical photonic states. These results suggest that the ratchet universality law seems essential for any \textit{optimal} application of the ratchet effect, particularly in the contexts of superconducting integrated power electronics, electron quantum optics, and quantum computing.

It is known that the Minkowski vacuum appears as a thermal medium to an accelerated observer due to the renowned Unruh effect. More recently, it has been shown that at least for lower-spin fields this medium also exhibits a non-zero "entanglement" shear viscosity, which saturates the fundamental Kovtun-Son-Starinets (KSS) bound. We test the universality of this result for higher spins by computing the entanglement viscosity for spin-3/2 fields within the Rarita-Schwinger-Adler (RSA) theory. Strikingly, we obtain a negative viscosity. However, computing the entropy density using the modular Hamiltonian expansion method, we find it is also negative, and the viscosity to entropy ratio saturates the KSS bound. To clarify the origin of the negativity, we use another approach of Zubarev density operator, which gives positive entropy. We also show that RSA theory has many features of a conformal field theory.

We study the deterministic reiterated homogenization of the non-stationary Navier-Stokes type equations in fixed domains with periodically rapidly varying coefficients. One convergence theorem and a corrector result are proved, and we derive the macroscopic homogenized model.

The ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients (ELEPHANT), has been developed as a framework for filtering hostless candidates, in real time alert systems, and implemented as a filter in the Fink broker. ELEPHANT works on stamps and requires minimal information, thus allowing for fast identification of extragalactic transient events. In this work we evaluate the performance of the ELEPHANT pipeline by systematically analyzing flagged hostless candidates identified between 1 September 2023 and 31 December 2025. Our goal is to quantifying its accuracy and identify dominant sources of contamination. For each flagged candidate we collected additional information from multiple catalogues and archival repositories. We further examined their light-curve evolution and astrometric consistency (coordinate dispersion over time) to refine source classification. Results. Out of 877 flagged events, 67 are confidently confirmed as genuinely hostless candidates, with no detectable host galaxy in either existing catalogues or archival imaging, representing a high-purity sample of intrinsically faint or absent hosts. Additional 51 events are linked to visually identifiable hosts that are entirely absent from both catalogues and ZTF stamps. For the confirmed hostless subset, the inferred upper limits on host-galaxy absolute magnitudes extend well below the luminosity range of typical dwarf galaxies. The pipeline showed an overall accuracy of 0.84, with the majority of the classified flagged events being Type Ia supernovae, and the second most detected class being Type I superluminous supernova. ELEPHANT has been adapted to deal with the Rubin alert stream and has been processing its alerts since February 2026.

Let K be a complete, non-archimedean valued field with a residue field of characteristic different from 2. A Whittaker group G is a discontinuous subgroup of PGL(2,K), freely generated by elements s_0,...,s_g of order two, each defined by a pair of fixed points {a_0,b_0},...,{a_g,b_g}. These fixed points are called ``in good position''. A subgroup W in G of index 2 is a Schottky group and produces a hyperelliptic Mumford curve Omega/W --> Omega/G = P^1, called `Whittaker curve', of genus g and with branch locus B in P^1(K). An explicit parametrization of Whittaker curves in terms of theta functions for W and G and the data of the fixed points, is developed. In particular, this allows one to express the branched points (and other data such as p-adic periods and p-adic heights) in terms of values of theta functions. A central theme of this paper is the relation between the fixed points and the branch locus. For a given configuration (P,m) of $g+1$ pairs of points in P^1, one defines a rigid space Fix_{P,m} of fixed points in good position with that configuration and a rigid space of branched points $ Branch_{P,m} in that configuration. A main result is that the natural morphism FB: Fix_{P,m} --> Branch_{P,m} is a rigid etale covering with Galois group {\pm 1}^{d-1} for some d>0. For all cases of genus g=2,3 (and for some more), an approximation of FB is computed which confirms the main result. Classification of Whittaker groups and analytic reductions of Whittaker curves is another important issue of this paper. The background material in this paper complements the work of L.~Gerritzen, G.~Van Steen, F.~Herrlich and others. It involves re-examination of some proofs, the derivation of properties of semi-stable analytic reductions and studying good position of fixed points.

We construct a scalar invariant of flat principal 2-bundles over 3-manifolds, with structure 2-group $\mathcal{G}$, from an involutory Hopf algebra graded by $\mathcal{G}$. Expressing $\mathcal{G}$ in terms of a crossed module $χ$ and using the classification of such 2-bundles via the classifying space $Bχ$, this amounts to constructing a homotopy invariant of maps from 3-manifolds to $Bχ$. The construction of the invariant relies on a combinatorial description of such maps by $χ$-colored Heegaard diagrams. When the corresponding map to $Bχ$ is nullhomotopic or, equivalently, when the associated flat principal $\mathcal{G}$-bundle is trivializable, the invariant reduces to the Kuperberg invariant of the underlying 3-manifold.

In \cite{BCO25}, Bruzzo, Capasso and Otero extended the notion of ampleness of vector bundles to the more general context of Higgs bundles. But the ampleness of Higgs bundles did not coincide with the ampleness of vector bundles when the Higgs field is zero. We modify the definition of ample Higgs bundles that results in removal of this discrepancy. Invoking this definition, we study various properties of Higgs ample vector bundles. In particular, we prove a Barton-Kleimann type criterion to characterize the Higgs ample vector bundles.

Detecting the redshifted global 21-cm signal from the cosmic dawn (CD) remains a major challenge due to strong terrestrial Radio Frequency Interference (RFI), particularly dominated by Frequency Modulation (FM) transmissions in the 88-110 MHz range. While observations from the radio-quiet lunar farside are ideal, Earth orbit offers an intermediate and simpler alternative that may mitigate several limitations of ground-based experiments. We assess the feasibility of detecting the global 21-cm signal from Earth orbit by quantifying FM-based RFI at different altitudes and orbital configurations. We present STARFIRE-2 (Simulation of TerrestriAl Radio Frequency Interference in oRbits around Earth -- 2), an algorithm that estimates FM transmitter-based RFI intercepted by radiometers in orbit. The model constructs a global FM transmitter database and compensates for incomplete data using statistical methods. Using PRATUSH as the reference experiment, we simulate a range of orbital scenarios to identify configurations that minimize RFI and optimize sensitivity for global 21-cm detection. The algorithm can also be adapted for other experiments. Simulations indicate that conducting such an experiment from Earth orbit is feasible for a thermal noise limited instrument placed in a low-Earth, near-polar orbit. Mock sky observations further demonstrate that most theoretically plausible cosmic dawn 21-cm signals can be recovered with high confidence under these optimized orbital conditions.

We study the athermal mechanical response of deformable ring assemblies to quasistatic compression. Beyond jamming, further densification induces buckling of rings, resulting in macroscopic mechanical softening. Under cyclic compression, monodisperse systems anneal toward a nearly reversible path passing through an ordered state, whereas polydisperse systems converge to stable, hysteretic limit cycles. These limit cycles encode a robust memory of the training history that is retained even under subsequent overdriving. We show that macroscopic hysteresis in the disordered packings originates from directionally asymmetric non-affine deformations at the microscale while keeping contact network largely intact. Our findings demonstrate how particle deformability governs collective self-organization and memory formation in jammed soft matter.

Let $\mathcal{F}_5$ denote the $3$-uniform hypergraph on the vertex set $\{f_1,f_2,\dots,f_5\}$ with hyperedges $\{f_1f_2f_3,f_1f_2f_4,f_3f_4f_5\}$. Recently, Balogh, Clemen and Luo determined the Turán number of a one-vertex blow-up of $\mathcal{F}_5$, more specifically, they blow up the vertex $f_5$ to $t$ vertices, the resulting hypergraph is denoted by $\mathcal{F}_5(f_5;t)$. They show that for infinitely many $t$, $\mathcal{F}_5(f_5;t)$ has exponentially many extremal constructions and positive Turán density. In this paper, we determine the exact Turán number of the hypergraph obtained by blowing up $f_3$ of $\mathcal{F}_5$ to $t$ vertices and show that it also has exponentially many extremal constructions. We also give a general upper bound and lower bound of the Turán number of every blow-up of $\mathcal{F}_5$. For some special blow-ups of $\mathcal{F}_5$, for example, $t$-disjoint copies of $\mathcal{F}_5$, we determine the exact Turán number. We construct a hypergraph $\mathcal{F}_{sim}(t)$ which is a subgraph of a blow-up of $\mathcal{F}_5$, and is contained in the hypergraph obtained by adding any new hyperedge to the Turán hypergraph (the balanced complete $3$-partite hypergraph), but its extremal construction is not the Turán hypergraph. We also determine the exact Turán number of $\mathcal{F}_{sim}(t)$.