Neural audio codecs (NACs) typically encode the short-term energy (gain) and normalized structure (shape) of speech/audio signals jointly within the same latent space. As a result, they are poorly robust to a global variation of the input signal level in the sense that such variation has strong influence on the embedding vectors at the output of the encoder and their quantization. This methodology is inherently inefficient, leading to codebook redundancy and suboptimal bitrate-distortion performance. To address these limitations, we propose to introduce shape-gain decomposition, widely used in classical speech/audio coding, into the NAC framework. The principle of the proposed Equalizer methodology is to decompose the input signal -- before the NAC encoder -- into gain and normalized shape vector on a short-term basis. The shape vector is processed by the NAC, while the gain is quantized with scalar quantization and transmitted separately. The output (decoded) signal is reconstructed from the normalized output of the NAC and the quantized gain. Our experiments conducted on speech signals show that this general methodology, easily applicable to any NAC, enables a substantial gain in
Photodiodes based on trap-assisted current injection can exhibit internal photomultiplication with apparent quantum efficiencies far exceeding unity, raising the question of whether such gain fundamentally enhances detector sensitivity. We employ a minimal analytical framework based on a single gain-active trapped state coupling photogenerated carriers to contact injection. The gain is intrinsically self-limiting: the injection process that amplifies the current simultaneously accelerates relaxation of the gain-enabling state, producing an inherently nonlinear, operating-point-dependent response. The form of this nonlinearity is not universal -- once the trap level is generalized to an energetic distribution and recombination is allowed to be bimolecular, the same mechanism yields superlinear, linear, or strongly sublinear responses. A single chord gain is therefore not a meaningful device descriptor, and chord-gain comparisons across the literature conflate devices in different regimes. Treating trap occupancy and injection as coupled stochastic processes, we show that internal gain introduces a strictly non-negative fluctuation penalty from the dissipative dynamics that sustain t
Masked Diffusion Models (MDMs) enable flexible decoding orders, yet existing samplers remain largely greedy, selecting locally certain tokens without accounting for their downstream effects. We show that this myopia can increase cumulative uncertainty and lead to suboptimal generation. To address this, we propose the **Info-Gain Sampler**, a training-free decoding method that uses the bidirectional structure of MDMs to balance immediate uncertainty with the information gained over remaining masked positions. Across reasoning, coding, creative writing, and image generation tasks, Info-Gain Sampler consistently outperforms existing MDM samplers, improving average reasoning accuracy by 2.9--11.6 percentage points and achieving a 62.8% average win rate in creative writing. The code is available at https://github.com/yks23/Information-Gain-Sampler.
A complex unit gain graph (or a $\mathbb{T}$-gain graph) $Θ(Σ,\varphi)$ is a graph where the unit complex number is assign by a function $\varphi$ to every oriented edge of $Σ$ and assign its inverse to the opposite orientation. In this paper, we define the two gain distance Laplacian matrices $DL^{\max}_{<}(Θ)$ and $DL^{\min}_{<}(Θ)$ corresponding to the two gain distance matrices $D^{\max}_{<}(Θ)$ and $D^{\min}_{<}(Θ)$ defined for $\mathbb{T}$-gain graphs $Θ(Σ,\varphi)$, for any vertex ordering $(V(Σ),<)$. Furthermore, we provide the characterization of singularity and find formulas for the rank of those Laplacian matrices. We also establish two types of characterization for balanced in complex unit gain graphs while using the gain distance Lapalcian matrices. Most of the results are derived by proving them more generally for weighted $\mathbb{T}$-gain graphs.
Conventional optical materials are characterized by either a dissipative response, which results in polarization-independent absorption, or by a gain response that leads to wave amplification. In this work, we study a peculiar class of materials with chiral-gain properties, where gain selectively amplifies waves of one polarization handedness, while dissipation suppresses the opposite handedness. We uncover a novel phenomenon, gain-momentum locking, at the boundary of chiral-gain media, where surface plasmons are amplified or attenuated based on their direction of propagation. This effect, driven by the interplay between spin-momentum locking and polarization-sensitive non-Hermitian responses, enables precise control over unidirectional wave propagation. Our findings open the door to photonic devices with unprecedented capabilities, such as lossless unidirectional edge-wave propagation and the generation of light with intrinsic orbital angular momentum.
It has been discovered before (arXiv:2306.07676) that for the selectivity gain due to fluctuations in the process of primary odor reception by olfactory receptor neuron (ORN) there exists an optimal concentration of odors at which increased selectivity is mostly manifested. We estimate by means of numerical simulation what could be the gain value at that concentration by modeling ORN as a leaky integrate-and-fire neuron with membrane populated by receptor proteins R which bind and release odor molecules randomly. Each R is modeled as a ligand-gated ion channel, and binding-releasing is modeled as a Markov stochastic process. Possible values for the selectivity gain are calculated for ORN parameters suggested by experimental data. Keywords: ORN, selectivity, receptor proteins, fluctuations, stochastic process, Markov process
We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of $G$-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group $G$. For instance, for two signed graphs, this notion of cospectrality is equivalent to the cospectrality of their signed adjacency matrices together with the cospectrality of their underlying graphs. Moreover, we introduce another more flexible switching in order to obtain pairs of gain graphs cospectral with respect to some fixed unitary representation. Many existing notions of spectrum for graphs and gain graphs are indeed special cases of these spectra associated with particular representations, therefore our construction recovers the classical Godsil-McKay switching and the Godsil-McKay switching for signed and complex unit gain graphs. As in the classical case, not all gain graphs are suitable for these switchings: we analyze the relationships between the properties that make the graph suitable for the one or the other switching. Finally we apply our construction in order to define a Godsil-McKay switching for the right spectrum of quaternion unit gain graphs.
We study transmission stabilization of optical solitons against emission of radiation in nonlinear optical waveguides in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. We first show how the collisional Raman frequency shift perturbation arises in three different physical setups. We then show by numerical simulations with a perturbed nonlinear Schrödinger (NLS) model that transmission in waveguides with weak frequency-independent linear gain is unstable. The radiative instability is stronger than the radiative instabilities that were observed in earlier studies for soliton transmission in the presence of weak linear gain, cubic loss, and various frequency-shifting physical mechanisms. In particular, the Fourier spectrum of the radiation is significantly more spiky and broadband than the radiation's Fourier spectra in earlier studies. Moreover, we demonstrate by numerical simulations with another perturbed NLS model that transmission in waveguides with weak frequency-dependent linear gain-loss, cubic loss, and the collisional Raman frequency shift is stable. Despite the stronger radiative instability in the corresponding waveguide setup
Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges. Generalizing the notion of gain graphs, skew gain graphs have the property that the gain of a reversed edge is the image of edge gain under an anti-involution. In this paper, we deal with the adjacency matrix of skew gain graphs with involutive automorphism on a field of characteristic zero and their charactersitic polynomials. Spectra of some particular skew gain graphs are also discussed. Meanwhile it is interesting to note that weighted graphs are particular cases of skew gain graphs.
A complex unit gain graph ($ \mathbb{T} $-gain graph), $ Φ=(G, \varphi) $ is a graph where the function $ \varphi $ assigns a unit complex number to each orientation of an edge of $ G $, and its inverse is assigned to the opposite orientation. %A complex unit gain graph($ \mathbb{T} $-gain graph) is a simple graph where each orientation of an edge is given a complex unit, and its inverse is assigned to the opposite orientation of the edge. In this article, we propose gain distance matrices for $ \mathbb{T} $-gain graphs. These notions generalize the corresponding known concepts of distance matrices and signed distance matrices. Shahul K. Hameed et al. introduced signed distance matrices and developed their properties. Motivated by their work, we establish several spectral properties, including some equivalences between balanced $ \mathbb{T} $-gain graphs and gain distance matrices. Furthermore, we introduce the notion of positively weighted $ \mathbb{T} $-gain graphs and study some of their properties. Using these properties, Acharya's and Stanić's spectral criteria for balance are deduced. Moreover, the notions of order independence and distance compatibility are studied. Besides,
The existing volumetric gain for robotic exploration is calculated in the 3D occupancy map, while the sampling-based exploration method is extended in the reachable (free) space. The inconsistency between them makes the existing calculation of volumetric gain inappropriate for a complete exploration of the environment. To address this issue, we propose a concave-hull based volumetric gain in a sampling-based exploration framework. The concave hull is constructed based on the viewpoints generated by Rapidly-exploring Random Tree (RRT) and the nodes that fail to expand. All space outside this concave hull is considered unknown. The volumetric gain is calculated based on the viewpoints configuration rather than using the occupancy map. With the new volumetric gain, robots can avoid inefficient or even erroneous exploration behavior caused by the inappropriateness of existing volumetric gain calculation methods. Our exploration method is evaluated against the existing state-of-the-art RRT-based method in a benchmark environment. In the evaluated environment, the average running time of our method is about 38.4% of the existing state-of-the-art method and our method is more robust.
A conjugate skew gain graph is a skew gain graph with the labels (also called, the conjugate skew gains) from the field of complex numbes on the oriented edges such that they get conjugated when we reverse the orientation. In this paper we introduce distance matrices for conjugate skew gain graphs and characterize balanced conjugate skew gain graphs using these matrices. We provide explicit formulae for the distance spectra of certain conjugate skew gain graphs.
Low Gain Avalanche Detectors(LGADs) is one of the candidate sensing technologies for future 4D-tracking applications and recently have been qualified to be used in the ATLAS and CMS timing detectors for the CERN High Luminosity Large Hadron Collider upgrade.LGADs can achieve an excellent timing performance by the presence of an internal gain that improves the signal-to-noise ratio leading to a better time resolution. These detectors are designed to exhibit a moderate gain with an increase of the reverse bias voltage. The value of the gain strongly depends on the temperature. Thus, these two values must be kept under control in the experiments to maintain the gain within the required values. A reduction in the reverse bias or an increase in the temperature will reduce the gain significantly. In this paper, a mechanism for gain suppression in LGADs is going to be presented. It was observed, that the gain measured in these devices depends on the charge density projected into the gain layer, generated by a laser or a charged particle in their bulk. Measurements performed with different detectors showed that ionizing processes that induce more charge density in the detector bulk lead to
Conditional computing processes an input using only part of the neural network's computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: Reducing the computational burden is an obvious advantage. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to take a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources.
We examine a measure of individual student gain by preservice elementary teachers, related to Richard Hakes use of mean gain in the study of reform classes in undergraduate physics. The gain statistic assesses the amount individual students increase their test scores from initial test to final test, as a proportion of the possible increase for each student. We examine the written work in mathematics classes of preservice elementary teachers with very high gain and those with very low gain and show that these groups exhibit distinct psychological attitudes and dispositions to learning mathematics. We show a statistically significant, small, increase in average gain when course goals focus on patterns, connections, and meaning making in mathematics. A common belief is that students with low initial test scores will have higher gains, and students with high initial-test scores will have lower gains. We show that this is not correct for a cohort of preservice elementary teachers.
Parity-time (PT) symmetry and broken in micro/nano photonic structures have been investigated extensively as they bring new opportunities to control the flow of light based on non-Hermitian optics. Previous studies have focused on the situations of PT-symmetry broken in loss-loss or gain-loss coupling systems. Here, we theoretically predict the gain-gain and gain-lossless PT-broken from phase diagram, where the boundaries between PT-symmetry and PT-broken can be clearly defined in the full-parameter space including gain, lossless and loss. For specific micro/nano photonic structures, such as coupled waveguides, we give the transmission matrices of each phase space, which can be used for beam splitting. Taking coupled waveguides as an example, we obtain periodic energy exchange in PT-symmetry phase and exponential gain or loss in PT-broken phase, which are consistent with the phase diagram. The scenario giving a full view of PT-symmetry or broken, will not only deepen the understanding of fundamental physics, but also will promote the breakthrough of photonic applications like optical routers and beam splitters.
We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg-Landau (GL) gain-loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled nonlinear Schrödinger (NLS) equations. The NN interaction property leads to the elimination of collisional three-pulse interaction effects, which prevented the observation of stable multisequence soliton propagation with J>2 sequences in the presence of generic GL gain-loss in all previous studies. We show that the dynamics of soliton amplitudes can be described by a generalized J-dimensional Lotka-Volterra (LV) model. Stability and bifurcation analysis for the equilibrium points of the LV model, which is augmented by an application of the Lyapunov function method, is used to develop setups that lead to robust and scalable transmission stabilization and switching for a general J value. The predictions of the LV model are confirmed by extensive numerical simulations with the perturbed coupled-NLS model with J=3, 4, and 5 soliton sequences. Furthermore, soliton stability and the agreement between the LV model's predictions and the simulations a
This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed of infinitely many finite-dimensional systems. We model these networks on infinite-dimensional $\ell_{\infty}$-type spaces. A crucial assumption in our results is that the internal Lyapunov gains, modeling the influence of the subsystems on each other, are linear functions. Moreover, the gain operator built from the internal gains is assumed to be subadditive and homogeneous, which covers both max-type and sum-type formulations for the ISS Lyapunov functions of the subsystems. As a consequence, the small-gain condition can be formulated in terms of a generalized spectral radius of the gain operator. Through an example, we show that the small-gain condition can easily be checked if the interconnection topology of the network has some kind of symmetry. While our main result provides an ISS Lyapunov function in implication form for the overall network, an ISS Lyapunov function in a dissipative form is constructed under mild extra assumptions.
In this contribution, we present an innovative design of the Low-Gain Avalanche Diode (LGAD) gain layer, the p$^+$ implant responsible for the local and controlled signal multiplication. In the standard LGAD design, the gain layer is obtained by implanting $\sim$ 5E16/cm$^3$ atoms of an acceptor material, typically Boron or Gallium, in the region below the n$^{++}$ electrode. In our design, we aim at designing a gain layer resulting from the overlap of a p$^+$ and an n$^+$ implants: the difference between acceptor and donor doping will result in an effective concentration of about 5E16/cm$^3$, similar to standard LGADs. At present, the gain mechanism of LGAD sensors under irradiation is maintained up to a fluence of $\sim$ 1-2E15/cm$^2$, and then it is lost due to the acceptor removal mechanism. The new design will be more resilient to radiation, as both acceptor and donor atoms will undergo removal with irradiation, but their difference will maintain constant. The compensated design will empower the 4D tracking ability typical of the LGAD sensors well above 1E16/cm$^2$.
This paper presents a fundamental relation between Output Asymptotic Gains (OAG) and Input-to-Output Stability (IOS) gains for linear systems. For any Input-to-State Stable, strictly causal linear system the minimum OAG is equal to the minimum IOS-gain. Moreover, both quantities can be computed by solving a specific optimal control problem and by considering only periodic inputs. The result is valid for wide classes of linear systems (involving delay systems or systems described by PDEs). The characterization of the minimum IOS-gain is important because it allows the non-conservative computation of the IOS-gains, which can be used in a small-gain analysis. The paper also presents a number of cases for finite-dimensional linear systems, where exact computation of the minimum IOS gain can be performed.