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We study minimum degree conditions that guarantee that an $n$-vertex graph is rigid in $\mathbb{R}^d$. For small values of $d$, we obtain a tight bound: for $d = O(\sqrt{n})$, every $n$-vertex graph with minimum degree at least $(n+d)/2 - 1$ is rigid in $\mathbb{R}^d$. For larger values of $d$, we achieve an approximate result: for $d = O(n/{\log^2}{n})$, every $n$-vertex graph with minimum degree at least $(n+2d)/2 - 1$ is rigid in $\mathbb{R}^d$. This bound is tight up to a factor of two in the coefficient of $d$. As a byproduct of our proof, we also obtain the following result, which may be of independent interest: for $d = O(n/{\log^2}{n})$, every $n$-vertex graph with minimum degree at least $d$ has pseudoachromatic number at least $d+1$; namely, the vertex set of such a graph can be partitioned into $d+1$ subsets such that there is at least one edge between each pair of subsets. This is tight., Comment: 18 pages

We study the maximum dimension $d=d(n,p)$ for which an Erd\H{o}s-R\'enyi $G(n,p)$ random graph is $d$-rigid. Our main results reveal two different regimes of rigidity in $G(n,p)$ separated at $p_c=C_*\log n/n,~C_*=2/(1-\log 2)$ -- the point where the graph's minimum degree exceeds half its average degree. We show that if $p < (1-\varepsilon)p_c $, then $d(n,p)$ is asymptotically almost surely (a.a.s.) equal to the minimum degree of $G(n,p)$. In contrast, if $p_c \leq p = o(n^{-1/2}) $ then $d(n,p) $ is a.a.s. equal to $(1/2 + o(1))np$. The second result confirms, in this regime, a conjecture of Krivelevich, Lew, and Michaeli.

We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together with constraints and objectives on the final program. Advanced synthesis algorithms transform the model into a low-level quantum program that meets the user's specification and is directed at a stipulated hardware. This separation of description from implementation is essential for scale. The technology adapts electronic design automation methods to quantum computing, finding feasible implementations in a virtually unlimited functional space. The results show clear superiority over the compilation and transpilation methods used today. We expect that this technological approach will take over and prevail as quantum software become more demanding, complex, and essential.

Instant Folded Strings (IFSs) are unconventional light strings that emerge when the string coupling increases with time. A particularly intriguing property of IFSs, especially relevant to cosmology, is that they violate the Null Energy Condition (NEC). In this paper, we begin to explore their cosmological effects. We find that NEC violation by IFSs is significantly suppressed in an expanding universe, leading to a universe that resembles our own, comprising matter, radiation, and dark energy. Upon closer examination, these components exhibit subtle, nonstandard traits that could be experimentally tested in the future. Notably, the origin of dark energy stems not only from the potential, as is usually the case, but also from the derivative of the potential with respect to the dilaton. This paves the way for a new approach to realizing inflation within string theory, addressing the Dine-Seiberg problem associated with dilaton stabilization, and perhaps even hinting at a novel mechanism to tackle the cosmological constant problem. Conversely, in a contracting universe, the effects of IFSs are amplified, making bouncing cosmologies a natural and prevalent outcome., Comment: 33 pages, 4 figures

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 Schr\"odinger (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 with weak linear gain, stabilization occurs via the same generic mechanism that was suggested in earlier studies. More precisely, the collisional Raman frequency shift experienced by the soliton leads to the separation of the soliton's and the radiation's Fourier spectra, while the frequency-dependent linear gain-loss leads to efficient suppression of radiation emission. Thus, our study demonstrates the robustness of the proposed generic soliton stabilization method, which is based on the interplay between perturbation-induced shifting of the soliton's frequency and frequency-dependent linear gain-loss., Comment: The paper demonstrates stabilization of optical solitons against radiation emission in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. It significantly extends the stabilization method that was proposed in arXiv:1804.03226 by showing that the proposed method works even when the underlying radiative instability due to linear gain is strong

We investigate the Peak-Power Limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems; however, its capacity is still unknown. We use a new geometry-based approach which evaluates the maximal entropy of the transmitted signal by assessing the volume of the body, in the space of Nyquist-rate samples, comprising all the points the transmitted signal can reach. This leads to lower bounds on capacity which are tight at high Signal to Noise Ratios (SNR). We found lower bounds on capacity, expressed as power efficiency, higher than the known ones by a factor of 3.35 and 8.6 in the low pass and the band pass cases respectively. The gap to the upper bounds is reduced to a power ratio of 1.5. The new bounds are numerically evaluated for FDMA-style signals with limited duration and also derived in the general case as a conjecture. The penalty in power efficiency due to the peak power constraint is roughly 6 dB at high SNR. Further research is needed to develop effective modulation and coding for this channel., Comment: A revised (minor revision) and shortened version was published in an open access journal, MDPI Entropy, https://doi.org/10.3390/e26121049

We present Jamba-1.5, new instruction-tuned large language models based on our Jamba architecture. Jamba is a hybrid Transformer-Mamba mixture of experts architecture, providing high throughput and low memory usage across context lengths, while retaining the same or better quality as Transformer models. We release two model sizes: Jamba-1.5-Large, with 94B active parameters, and Jamba-1.5-Mini, with 12B active parameters. Both models are fine-tuned for a variety of conversational and instruction-following capabilties, and have an effective context length of 256K tokens, the largest amongst open-weight models. To support cost-effective inference, we introduce ExpertsInt8, a novel quantization technique that allows fitting Jamba-1.5-Large on a machine with 8 80GB GPUs when processing 256K-token contexts without loss of quality. When evaluated on a battery of academic and chatbot benchmarks, Jamba-1.5 models achieve excellent results while providing high throughput and outperforming other open-weight models on long-context benchmarks. The model weights for both sizes are publicly available under the Jamba Open Model License and we release ExpertsInt8 as open source., Comment: Webpage: https://www.ai21.com/jamba

With the popularity of cellular phones, events are often recorded by multiple devices from different locations and shared on social media. Several different recordings could be found for many events. Such recordings are usually noisy, where noise for each device is local and unrelated to others. This case of multiple microphones at unknown locations, capturing local, uncorrelated noise, was rarely treated in the literature. In this work we propose a simple and effective crowdsourced audio enhancement method to remove local noises at each input audio signal. Then, averaging all cleaned source signals gives an improved audio of the event. We demonstrate the effectiveness of our method using synthetic audio signals, together with real-world recordings. This simple approach can set a new baseline for crowdsourced audio enhancement for more sophisticated methods which we hope will be developed by the research community.

Soundness of a type system is a fundemental property that guarantees that no operation that is not supported by a value will be performed on that value at run time. A type checker for a sound type system is expected to issue a warning on every type error. While soundness is a desirable property for many practical applications, in 2016, Amin and Tate presented the first unsoundness proof for two major industry languages: Java and Scala. This proof relied on use-site variance and implicit null values. We present an unsoundness proof for Kotlin, another emerging industry language, which relies on a previously unknown unsound combination of language features. Kotlin does not have implicit null values, meaning that the proof by Amin and Tate would not work for Kotlin. Our new proof, which is an infringing code snippet, utilizes Kotlin's \emph{declaration-site} variance specification and does not require implicit null values. We present this counterexample to soundness in full along with detailed explanations of every step. Finally, we present a thorough discussion on precisely which language features cause this issue, as well as how Kotlin's compiler can be patched to fix it.

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic gradient descent (SGD) and a possible simplicity bias arising from the neural network architecture. The goal of this paper is to disentangle the factors that influence generalization stemming from optimization and architectural choices by studying random and SGD-optimized networks that achieve zero training error. We experimentally show, in the low sample regime, that overparameterization in terms of increasing width is beneficial for generalization, and this benefit is due to the bias of SGD and not due to an architectural bias. In contrast, for increasing depth, overparameterization is detrimental for generalization, but random and SGD-optimized networks behave similarly, so this can be attributed to an architectural bias. For more information, see https://bias-sgd-or-architecture.github.io ., Comment: Accepted at ICML 2024

We study the question of whether a sequence d = (d_1,d_2, \ldots, d_n) of positive integers is the degree sequence of some outerplanar (a.k.a. 1-page book embeddable) graph G. If so, G is an outerplanar realization of d and d is an outerplanaric sequence. The case where \sum d \leq 2n - 2 is easy, as d has a realization by a forest (which is trivially an outerplanar graph). In this paper, we consider the family \cD of all sequences d of even sum 2n\leq \sum d \le 4n-6-2\multipl_1, where \multipl_x is the number of x's in d. (The second inequality is a necessary condition for a sequence d with \sum d\geq 2n to be outerplanaric.) We partition \cD into two disjoint subfamilies, \cD=\cD_{NOP}\cup\cD_{2PBE}, such that every sequence in \cD_{NOP} is provably non-outerplanaric, and every sequence in \cD_{2PBE} is given a realizing graph $G$ enjoying a 2-page book embedding (and moreover, one of the pages is also bipartite)., Comment: This paper has published in 35th IWOCA

We argue that on-shell excitations with large negative energies are created rapidly when the string coupling increases with time. This does not indicate an inconsistency in string theory since the negative energy on-shell excitation is always entangled with an on-shell excitation with a positive energy. The total energy of this energy-EPR state vanishes. We discuss the reason the energy-EPR states appear in string theory and the role they might play in black hole physics., Comment: 11 pages, 2 figures

We define a structure of an algebra on the Lagrangian Floer cohomology of a Lagrangian submanifold over the quantum cohomology of the ambient symplectic manifold. The structure is analogous to the one defined by Biran-Cornea, but is constructed in the differential forms model. In the spirit of Ganatra and Hugtenburg, we define another such algebra structure using a closed-open map. We show that the two structures coincide. As an application, we show that the module structure for the 2-dimensional Clifford torus is given by multiplication by a Novikov coefficient, similarly to the Biran-Cornea module structure for this case., Comment: 65 pages, 3 figures

Digital Behavior Change Interventions (DBCIs) are supporting development of new health behaviors. Evaluating their effectiveness is crucial for their improvement and understanding of success factors. However, comprehensive guidance for developers, particularly in small-scale studies with ethical constraints, is limited. Building on the CAPABLE project, this study aims to define effective engagement with DBCIs for supporting cancer patients in enhancing their quality of life. We identify metrics for measuring engagement, explore the interest of both patients and clinicians in DBCIs, and propose hypotheses for assessing the impact of DBCIs in such contexts. Our findings suggest that clinician prescriptions significantly increase sustained engagement with mobile DBCIs. In addition, while one weekly engagement with a DBCI is sufficient to maintain well-being, transitioning from extrinsic to intrinsic motivation may require a higher level of engagement.

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 Schr\"odinger (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 are independent of J. Therefore, our study provides the first demonstration of robust control of multiple colliding sequences of NLS solitons in the presence of generic weak GL gain-loss with an arbitrary number of sequences. Due to the robustness and scalability of the results, they can have important applications in stabilization and switching of broadband soliton-based optical waveguide transmission., Comment: 46 pages, 15 figures. The paper provides the first demonstration of robust control of multiple soliton sequences of the NLS equation in the presence of generic GL gain-loss with an arbitrary number of sequences. It significantly extends the results of all previous works on the topic, which were limited to two-sequence transmission or to transmission with nongeneric GL gain-loss

Acoustic-directed assembly is a modular and flexible bottom-up technique with the potential to pattern a wide range of materials. Standing acoustic waves have been previously employed for patterning preformed metal particles, however, direct patterning of metallic structures from precursors remains unexplored. Here, we investigate utilization of standing waves to exert control over chemical reaction products, while also exploring their potential in the formation of multi-layered and composite micro-structures. Periodic metallic micro-structures were formed in a single step, simplifying microstructure fabrication. Concentric structures were obtained by introducing a metal precursor salt and a reducing agent into a cylindrical piezoelectric resonator that also served as a reservoir. In addition, we introduce an innovative approach to directly fabricate metallic multi-layer and composite structures by reducing different metal ions or adding nanoparticles during the reduction step. Fewer steps are needed, compared with other methods, and there is no need to stabilize the nanoparticles or to ensure chemical affinity between the metallic matrix and inorganic nanoparticles. This innovative approach is promising for production of complex microstructures with enhanced functionality and controlled properties.

A graph is called $d$-rigid if there exists a generic embedding of its vertex set into $\mathbb{R}^d$ such that every continuous motion of the vertices that preserves the lengths of all edges actually preserves the distances between all pairs of vertices. The rigidity of a graph is the maximal $d$ such that the graph is $d$-rigid. We present new sufficient conditions for the $d$-rigidity of a graph in terms of the existence of ``rigid partitions'' -- partitions of the graph that satisfy certain connectivity properties. This extends previous results by Crapo, Lindemann, and Lew, Nevo, Peled and Raz. As an application, we present new results on the rigidity of highly-connected graphs, random graphs, random bipartite graphs, pseudorandom graphs, and dense graphs. In particular, we prove that random $C d\log d$-regular graphs are typically $d$-rigid, demonstrate the existence of a giant $d$-rigid component in sparse random binomial graphs, and show that the rigidity of relatively sparse random binomial bipartite graphs is roughly the same as that of the complete bipartite graph, which we consider an interesting phenomenon. Furthermore, we show that a graph admitting $\binom{d+1}{2}$ disjoint connected dominating sets is $d$-rigid. This implies a weak version of the Lov\'asz--Yemini conjecture on the rigidity of highly-connected graphs. We also present an alternative short proof for a recent result by Lew, Nevo, Peled, and Raz, which asserts that the hitting time for $d$-rigidity in the random graph process typically coincides with the hitting time for minimum degree $d$., Comment: 30 pages. In this updated version, we have added a theorem concerning the rigidity of dense graphs and incorporated references to Vill\'anyi's recent resolution of the Lov\'asz-Yemini conjecture

Evidence-based medicine promises to improve the quality of healthcare by empowering medical decisions and practices with the best available evidence. The rapid growth of medical evidence, which can be obtained from various sources, poses a challenge in collecting, appraising, and synthesizing the evidential information. Recent advancements in generative AI, exemplified by large language models, hold promise in facilitating the arduous task. However, developing accountable, fair, and inclusive models remains a complicated undertaking. In this perspective, we discuss the trustworthiness of generative AI in the context of automated summarization of medical evidence.

Ontologies play a crucial role in organizing and representing knowledge. However, even current ontologies do not encompass all relevant concepts and relationships. Here, we explore the potential of large language models (LLM) to expand an existing ontology in a semi-automated fashion. We demonstrate our approach on the biomedical ontology SNOMED-CT utilizing semantic relation types from the widely used UMLS semantic network. We propose a method that uses conversational interactions with an LLM to analyze clinical practice guidelines (CPGs) and detect the relationships among the new medical concepts that are not present in SNOMED-CT. Our initial experimentation with the conversational prompts yielded promising preliminary results given a manually generated gold standard, directing our future potential improvements., Comment: Presented as a short paper at the Knowledge Representation for Healthcare 2023 workshop

Qubits based on ions trapped in linear radio-frequency traps form a successful platform for quantum computing, due to their high fidelity of operations, all-to-all connectivity and degree of local control. In principle there is no fundamental limit to the number of ion-based qubits that can be confined in a single 1D register. However, in practice there are two main issues associated with long trapped-ion crystals, that stem from the 'softening' of their modes of motion, upon scaling up: high heating rates of the ions' motion, and a dense motional spectrum; both impede the performance of high-fidelity qubit operations. Here we propose a holistic, scalable architecture for quantum computing with large ion-crystals that overcomes these issues. Our method relies on dynamically-operated optical potentials, that instantaneously segment the ion-crystal into cells of a manageable size. We show that these cells behave as nearly independent quantum registers, allowing for parallel entangling gates on all cells. The ability to reconfigure the optical potentials guarantees connectivity across the full ion-crystal, and also enables efficient mid-circuit measurements. We study the implementation of large-scale parallel multi-qubit entangling gates that operate simultaneously on all cells, and present a protocol to compensate for crosstalk errors, enabling full-scale usage of an extensively large register. We illustrate that this architecture is advantageous both for fault-tolerant digital quantum computation and for analog quantum simulations.