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Token prediction stability remains a challenge in autoregressive generative models, where minor variations in early inference steps often lead to significant semantic drift over extended sequences. A structured modulation mechanism was introduced to regulate hidden state transitions, ensuring that latent representation trajectories remain aligned with prior contextual dependencies while preserving generative flexibility. The modulation framework was designed to function within transformer-based architectures, dynamically constraining representation evolution without imposing external memory dependencies or extensive architectural modifications. Empirical evaluations demonstrated that structured latent adjustments contributed to reductions in perplexity fluctuations, entropy variance, and lexical instability, improving coherence in long-form text generation. Gradient propagation stability was further analyzed, revealing that the modulation process led to smoother optimization pathways, mitigating erratic fluctuations in weight updates across successive inference steps. The computational efficiency of the modulation process was assessed, showing that its integration within transformer-based architectures introduced only marginal overhead while maintaining compatibility with existing optimization frameworks. The structured modulation constraints also influenced syntactic variation, preventing excessive repetition while maintaining balanced sentence length distributions. Comparative evaluations against baseline models reinforced the role of controlled latent state evolution in improving pronoun resolution, logical consistency, and contextual alignment across autoregressive text generation tasks.

To identify what types of non-Fermi liquid (NFL) behavior are most likely to occur in cubic metals due to doublet impurities, we derive every cubic symmetry-allowed, NFL, Kondo-type exchange coupling. We find three distinct types of NFL behavior: two-channel Kondo (2CK) behavior for a non-Kramers doublet impurity coupled to local $\Gamma_8$ conduction electrons; topological Kondo physics for a Kramers doublet impurity and $\Gamma_4$ or $\Gamma_5$ conduction electrons; and lastly, spin-half impurity spin-$\frac{3}{2}$ conduction electron Kondo behavior for a Kramers doublet impurity and $\Gamma_8$ conduction electrons. The first two critical behaviors are not straightforward to realize. In the first case, 2CK physics is not guaranteed, since cubic symmetry does not prevent an effective spatial anisotropy from exceeding the 2CK coupling, which restores a Fermi liquid behavior. In the second case, the topological Kondo interaction is guaranteed to dominate, however, the spin degeneracy of the conduction electrons needs to be lifted e.g. by a magnetic field$-$so that they can be represented by $\Gamma_4$ or $\Gamma_5$ triplets$-$which then also lifts the degeneracy of the Kramers doublet. We find that the spin-half impurity spin-$\frac{3}{2}$ conduction electron, NFL, Kondo behavior has the greatest chance of existing in diluted, cubic compounds. We compute the thermodynamics of the topological Kondo model using the numerical renormalization group, and discuss the thermodynamics of the spin-half impurity spin-$\frac{3}{2}$ conduction electron Kondo model. We also identify candidate materials where the corresponding NFL behaviors could be observed., Comment: 6 pages + 2 pages of supplemental material, 1 figure

Despite intense experimental efforts, the nature of the unconventional superconducting order parameter of UTe$_2$ remains elusive. This puzzle stems from different reported numbers of superconducting transitions at ambient pressure, as well as a complex pressure-temperature phase diagram. To bring new insights into the superconducting properties of UTe$_2$, we measured the heat capacity and electrical resistivity of single crystals under compressive uniaxial stress $\sigma$ applied along different crystallographic directions. We find that the critical temperature $T_{\rm c}$ of the single observed bulk superconducting transition decreases with $\sigma$ along $[100]$ and $[110]$ but increases with $\sigma$ along $[001]$. Aside from its effect on $T_{\rm c}$, we notice that $c$-axis stress leads to a significant piezoresistivity, which we associate with the shift of the zero-pressure resistivity peak at $T^\star \approx 15\, \rm K$ to lower temperatures under stress. Finally, we show that an in-plane shear stress $\sigma_{xy}$ does not induce any observable splitting of the superconducting transition over a stress range of $\sigma_{xy}\approx 0.17 \, \rm GPa$. This result suggests that the superconducting order parameter of UTe$_2$ may be single-component at ambient pressure.

Low-lying coastal cities across the world are vulnerable to the combined impact of rainfall and storm tide. However, existing approaches lack the ability to model the combined effect of these flood mechanisms. Thus, to increase flood resilience, modeling techniques to improve understanding and prediction of the combined effect of these flood hazards are critical. To address this need, this study presents a modeling system for assessing the combined flood risk to coastal cities under changing climate conditions that leverages ocean modeling with land surface modeling capable of resolving urban drainage infrastructure within the city. The modeling approach is demonstrated in quantifying the future impact on transportation infrastructure within Norfolk, Virginia USA. A series of combined storms events are modeled for current (2020) and projected future (2070) climate conditions. Results show that pluvial flooding causes a larger interruption to the transportation network compared to tidal flooding under current climate conditions. By 2070, however, tidal flooding will be the dominant flooding mechanism with even nuisance flooding expected to happen daily due to SLR. In 2070, nuisance flooding is expected to cause a 4.6% total link close time (TLC), which is more than two times that of a 50-year storm surge (1.8% TLC) in 2020. The coupled model was compared with a widely used but physically simplistic bathtub method to assess the difference resulting from the more complex modeling presented. Results show that the bathtub method overestimated the flooded area near the shoreline by 9.5% and 3.1% for a 10-year storm surge event in 2020 and 2070, respectively, but underestimated flooded area in the inland region by 9.0% and 4.0% for the same events. The findings demonstrate the benefit of sophisticated modeling methods in climate adaptive planning and policy in coastal communities.

Newly-discovered superconductor UTe$_2$ is a strong contender for a topological spin-triplet state wherein a multi-component order parameter arises from two nearly-degenerate superconducting states. A key issue is whether both of these states intrinsically exist at ambient pressure. Through thermal expansion and calorimetry, we show that UTe$_2$ at ambient conditions exhibits two detectable transitions only in some samples, and the size of the thermal expansion jump at each transition varies when the measurement is performed in different regions of the sample. This result indicates that the two transitions arise from two spatially separated regions that are inhomogeneously mixed throughout the volume of the sample, each with a discrete superconducting transition temperature (T$_c$). Notably, samples with higher T$_c$ only show a single transition at ambient pressure. Above 0.3 GPa, however, two transitions are invariably observed in ac calorimetry. Our results not only point to a nearly vertical line in the pressure-temperature phase diagram but also provide a unified scenario for the sample dependence of UTe$_{2}$., Comment: 6 pages, 4 figures, includes supplemental information, changed conclusion on the origin of double-transition feature observed in some UTe2 samples

The theory of quantum order-by-disorder (QOBD) explains the formation of modulated magnetic states at the boundary between ferromagnetism and paramagnetism in zero field. PrPtAl has been argued to provide an archetype for this. Here, we report the phase diagram in magnetic field, applied along both the easy $a$-axis and hard $b$-axis. For field aligned to the $b$-axis, we find that the magnetic transition temperatures are suppressed and at low temperature there is a single modulated fan state, separating an easy $a$-axis ferromagnetic state from a field polarised state. This fan state is well explained with the QOBD theory in the presence of anisotropy and field. Experimental evidence supporting the QOBD explanation is provided by the large increase in the $T^2$ coefficient of the resistivity and direct detection of enhanced magnetic fluctuations with inelastic neutron scattering, across the field range spanned by the fan state. This shows that the QOBD mechanism can explain field induced modulated states that persist to very low temperature., Comment: Main text; 6 pages and 4 figures. Supplementary information; 10 pages and 5 figures

Stoichiometric SnTe is theoretically a small gap semiconductor that undergoes a ferroelectric distortion on cooling. In reality however, crystals are always non-stoichiometric and metallic; the ferroelectric transition is therefore more accurately described as a polar structural transition. Here we study the Fermi surface using quantum oscillations as a function of pressure. We find the oscillation spectrum changes at high pressure, due to the suppression of the polar transition and less than 10 kbar is sufficient to stabilize the undistorted cubic lattice. This is accompanied by a large decrease in the Hall and electrical resistivity. Combined with our density functional theory (DFT) calculations and angle resolved photoemission spectroscopy (ARPES) measurements this suggests the Fermi surface $L$-pockets have lower mobility than the tubular Fermi surfaces that connect them. Also captured in our DFT calculations is a small widening of the band gap and shift in density of states for the polar phase. Additionally we find the unusual phenomenon of a linear magnetoresistance that exists irrespective of the distortion that we attribute to regions of the Fermi surface with high curvature., Comment: 8 pages, 5 figures

Objective: to develop quantitative methods for the clinical interpretation of the ballistocardiogram (BCG). Methods: a closed-loop mathematical model of the cardiovascular system is proposed to theoretically simulate the mechanisms generating the BCG signal, which is then compared with the signal acquired via accelerometry on a suspended bed. Results: simulated arterial pressure waveforms and ventricular functions are in good qualitative and quantitative agreement with those reported in the clinical literature. Simulated BCG signals exhibit the typical I, J, K, L, M and N peaks and show good qualitative and quantitative agreement with experimental measurements. Simulated BCG signals associated with reduced contractility and increased stiffness of the left ventricle exhibit different changes that are characteristic of the specific pathological condition. Conclusion: the proposed closed-loop model captures the predominant features of BCG signals and can predict pathological changes on the basis of fundamental mechanisms in cardiovascular physiology. Significance: this work provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present study considers an average human body and can potentially be extended to include variability among individuals.

We discuss certain identities involving $\mu(n)$ and $M(x)=\sum_{n\leq x}\mu(n)$, the functions of M\"{o}bius and Mertens. These identities allow calculation of $M(N^d)$, for $d=2,3,4,\ldots\ $, as a sum of $O_d \left( N^d(\log N)^{2d - 2}\right)$ terms, each a product of the form $\mu(n_1) \cdots \mu(n_r)$ with $r\leq d$ and $n_1,\ldots , n_r\leq N$. We prove a more general identity in which $M(N^d)$ is replaced by $M(g,K)=\sum_{n\leq K}\mu(n)g(n)$, where $g(n)$ is an arbitrary totally multiplicative function, while each $n_j$ has its own range of summation, $1,\ldots , N_j$. We focus on the case $d=2$, $K=N^2$, $N_1=N_2=N$, where the identity has the form $M(g,N^2) = 2 M(g,N) - {\bf m}^{\rm T} A {\bf m}$, with $A$ being the $N\times N$ matrix of elements $a_{mn}=\sum _{k \leq N^2 /(mn)}\,g(k)$, while ${\bf m}=(\mu (1)g(1),\ldots ,\mu (N)g(N))^{\rm T}$. Our results in Sections 2 and 3 assume, moreover, that $g(n)$ equals $1$ for all $n$. In this case the Perron-Frobenius theorem applies: we find that $A$ has an eigenvalue that is approximately $(\pi^2 /6)N^2$, with eigenvector approximately ${\bf f} = (1,1/2,1/3,\ldots ,1/N)^{\rm T}$, and that, for large $N$, the second-largest eigenvalue lies in $(-0.58 N, -0.49 N)$. Estimates for the traces of $A$ and $A^2$ are obtained. We discuss ways to approximate ${\bf m}^{\rm T} A {\bf m}$, using the spectral decomposition of $A$, or Perron's formula: the latter approach leads to a contour integral involving the Riemann zeta-function. We also discuss using the identity $A = N^{2\,} {\bf f}^{\,} \!{\bf f}^T - \textstyle{1\over 2} {\bf u} {\bf u}^T + Z$, where ${\bf u} = (1,\ldots ,1)^{\rm T}$ and $Z$ is the $N\times N$ matrix of elements $z_{mn} = - \psi(N^2 / (mn))$, with $\psi(x)=x - \lfloor x\rfloor - \textstyle{1\over 2}$., Comment: 14 Pages, Plain TeX, submitted to Chebyshevski\u{i} Sb

The $j$th divisor function $d_j$, which counts the ordered factorisations of a positive integer into $j$ positive integer factors, is a very well-known arithmetic function; in particular, $d_2(n)$ gives the number of divisors of $n$. However, the $j$th non-trivial divisor function $c_j$, which counts the ordered proper factorisations of a positive integer into $j$ factors, each of which is greater than or equal to 2, is rather less well-studied. We also consider associated divisor functions $c_j^{(r)}$, whose definition is motivated by the sum-over divisors recurrence for $d_j$. After reviewing properties of $d_j$, we study analogous properties of $c_j$ and $c_j^{(r)}$, specifically regarding their Dirichlet series and generating functions, as well as representations in terms of binomial coefficient sums and hypergeometric series. We also express their ratios as binomial coefficient sums and hypergeometric series, and find explicit Dirichlet series and Euler products in some cases. As an illustrative application of the non-trivial and associated divisor functions, we show how they can be used to count principal reversible square matrices of the type considered by Ollerenshaw and Br\'ee, and hence sum-and-distance systems of integers.

A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic progression. Such systems, with two component sets, arise naturally in the study of matrices with symmetry properties and consecutive integer entries. Sum systems are an analogous concept where only sums of elements are considered. We establish a bijection between sum systems and sum-and-distance systems of corresponding size, and show that sum systems are equivalent to principal reversible cuboids, which are tensors with integer entries and a symmetry of "reversible square" type. We prove a structure theorem for principal reversible cuboids, which gives rise to an explicit construction formula for all sum systems in terms of joint ordered factorisations of their component set cardinalities.

Analyzing temperature dependent photoemission (PE) data of the ferromagnetic Kondo-lattice (KL) system YbNiSn in the light of the Periodic Anderson model (PAM) we show that the KL behavior is not limited to temperatures below a temperature T_K, defined empirically from resistivity and specificic heat measurements. As characteristic for weakly hybridized Ce and Yb systems, the PE spectra reveal a 4f-derived Fermi level peak, which reflects contributions from the Kondo resonance and its crystal electric field (CEF) satellites. In YbNiSn this peak has an unusual temperature dependence: With decreasing temperature a steady linear increase of intensity is observed which extends over a large interval ranging from 100 K down to 1 K without showing any peculiarities in the region of T_K ~ TC= 5.6 K. In the light of the single-impurity Anderson model (SIAM) this intensity variation reflects a linear increase of 4f occupancy with decreasing temperature, indicating an onset of Kondo screening at temperatures above 100 K. Within the PAM this phenomenon could be described by a non-Fermi liquid like T- linear damping of the self-energy which accounts phenomenologically for the feedback from the closely spaced CEF-states., Comment: Accepted to Phys. Rev. B

We report that the lowest energy transverse-optic phonon in metallic SnTe softens to near zero energy at the structural transition at $T_C=75 \text{~K}$ and importantly show that the energy of this mode below $T_C$ increases as the temperature decreases. Since the mode is a polar displacement this proves unambiguously that SnTe undergoes a ferroelectric displacement below $T_C$. Concentration gradients and imperfect stoichiometry in large crystals may explain why this was not seen in previous inelastic neutron scattering studies. Despite SnTe being metallic we find that the ferroelectric transition is similar to that in ferroelectric insulators, unmodified by the presence of conduction electrons: we find that (i) the damping of the polar mode is dominated by coupling to acoustic phonons rather than electron-phonon coupling (ii) the transition is almost an ideal continuous transition (iii) comparison with density functional calculations identifies the importance of dipolar-dipolar screening for understanding this behaviour., Comment: 5 pages main text with 4 figures. 5 pages of supplementary material with 7 figures

It is often said that the number of current world leaders who chose to be educated in another country can serve as a useful, though rough and incomplete, indicator of "soft power." So, since 2015, the Higher Education Policy Institute (HEPI) has been publishing desk research on the tertiary education of serving heads of state and heads of government. This Policy Note shows that the United Kingdom (UK) continues to fall behind the United States (US) when it comes to educating people who go on to lead their own countries.