Search

We study a simple one dimensional sluggish random walk model with subdiffusive growth. In the continuum hydrodynamic limit, the model corresponds to a particle diffusing on a line with a space dependent diffusion constant D(x)= |x|^{-\alpha} and a drift potential U(x)=|x|^{-\alpha}, where \alpha\geq 0 parametrizes the model. For \alpha=0 it reduces to the standard diffusion, while for \alpha>0 it leads to a slow subdiffusive dynamics with the distance scaling as x\sim t^{\mu} at late times with \mu= 1/(\alpha+2)\leq 1/2. In this paper, we compute exactly, for all \alpha\ge 0, the full probability distributions of three observables for a sluggish walker of duration T starting at the origin: (i) the occupation time t_+ denoting the time spent on the positive side of the origin, (ii) the last passage time t_{\rm l} through the origin before T, and (iii) the time t_M at which the walker is maximally displaced on the positive side of the origin. We show that while for \alpha=0 all three distributions are identical and exhibit the celebrated arcsine laws of L\'evy, they become different from each other for any \alpha>0 and have nontrivial shapes dependent on \alpha. This generalizes the L\'evy's three arcsine laws for normal diffusion (\alpha=0) to the subdiffusive sluggish walker model with a general \alpha\geq 0. Numerical simulations are in excellent agreement with our analytical predictions., Comment: 27 pages, 8 Figures

In myoelectric control, simultaneous control of multiple degrees of freedom can be challenging due to the dexterity of the human hand. Numerous studies have focused on hand functionality, however, they only focused on a few degrees of freedom. In this paper, a 3DCNN-MLP model is proposed that uses high-density sEMG signals to estimate 20 hand joint positions and grip force simultaneously. The deep learning model maps the muscle activity to the hand kinematics and kinetics. The proposed models' performance is also evaluated in estimating grip forces with real-time resolution. This paper investigated three individual dynamic hand movements (2pinch, 3pinch, and fist closing and opening) while applying forces in 10% and 30% of the maximum voluntary contraction (MVC). The results demonstrated significant accuracy in estimating kinetics and kinematics. The average Euclidean distance across all joints and subjects was 11.01 $\pm$ 2.22 mm and the mean absolute error for offline and real-time force estimation were found to be 0.8 $\pm$ 0.33 N and 2.09 $\pm$ 0.9 N respectively. The results demonstrate that by leveraging high-density sEMG and deep learning, it is possible to estimate human hand dynamics (kinematics and kinetics), which is a step forward to practical prosthetic hands.

Sensitivity and resolution of space telescopes are directly related to the size of the primary mirror. Enabling such future extremely large space telescopes or even arrays of those will require to drastically reduce the areal weight of the mirror system. Utilizing a thin parabolic polymeric membrane as primary mirror offers the prospect of very low weight and the flexible nature of those membranes allows compactly store them upon launch. Upon deployment the structure is unfolded and the mirror shape restored. Being an extremely thin structure, an active shape correction is required. Utilizing a thermal control of the surface via radiative coupling, localized shape changes are imprinted into the membrane telescope. In this paper we present the modelling and experimental test of the radiative adaptive optics. A detailed modeling of the influence function of the radiative shaping onto the membrane mirror has been carried out. Experimentally we have been radiatively actuated the shape of a prototype mirror in closed loop with a wavefront sensor and proven that we can control the mirrors surface figure to a ~15nm RMS precision., Comment: 13 pages

Starting from a uniquely ergodic action of a locally compact group $G$ on a compact space $X_0$, we consider non-commutative skew-product extensions of the dynamics, on the crossed product $C(X_0)\rtimes_\alpha\mathbb{Z}$, through a $1$-cocycle of $G$ in $\mathbb{T}$, with $\alpha$ commuting with the given dynamics. We first prove that any such two skew-product extensions are conjugate if and only if the corresponding cocycles are cohomologous. We then study unique ergodicity and unique ergodicity w.r.t. the fixed-point subalgebra by characterizing both in terms of the cocycle assigning the dynamics. The set of all invariant states is also determined: it is affinely homeomorphic with $\mathcal{P}(\mathbb{T})$, the Borel probability measures on the one-dimensional torus $\mathbb{T}$, as long as the system is not uniquely ergodic. Finally, we show that unique ergodicity w.r.t. the fixed-point subalgebra of a skew-product extension amounts to the uniqueness of an invariant conditional expectation onto the fixed-point subalgebra, Comment: 28 pages

The discovery of CRISPR-mediated gene activation (CRISPRa) has transformed the way in which we perform genetic screening, bioproduction and therapeutics through its ability to scale and multiplex. However, the emergence of loads on the key molecular resources constituting CRISPRa by the orthogonal short RNA that guide such resources to gene targets, couple theoretically independent CRISPRa modules. This coupling negates the ability of CRISPRa systems to concurrently regulate multiple genes independent of one another. In this paper, we propose to reduce this coupling by mitigating the loads on the molecular resources that constitute CRISPRa. In particular, we design a multi-variable controller that makes the concentration of these molecular resources robust to variations in the level of the short RNA loads. This work serves as a foundation to design and implement CRISPRa controllers for practical applications., Comment: 9 pages, 7 figures, IEEE CDC 2024

Restoring limb motor function in individuals with spinal cord injury (SCI), stroke, or amputation remains a critical challenge, one which affects millions worldwide. Recent studies show through surface electromyography (EMG) that spared motor neurons can still be voluntarily controlled, even without visible limb movement . These signals can be decoded and used for motor intent estimation; however, current wearable solutions lack the necessary hardware and software for intuitive interfacing of the spared degrees of freedom after neural injuries. To address these limitations, we developed a wireless, high-density EMG bracelet, coupled with a novel software framework, MyoGestic. Our system allows rapid and tailored adaptability of machine learning models to the needs of the users, facilitating real-time decoding of multiple spared distinctive degrees of freedom. In our study, we successfully decoded the motor intent from two participants with SCI, two with spinal stroke , and three amputees in real-time, achieving several controllable degrees of freedom within minutes after wearing the EMG bracelet. We provide a proof-of-concept that these decoded signals can be used to control a digitally rendered hand, a wearable orthosis, a prosthesis, or a 2D cursor. Our framework promotes a participant-centered approach, allowing immediate feedback integration, thus enhancing the iterative development of myocontrol algorithms. The proposed open-source software framework, MyoGestic, allows researchers and patients to focus on the augmentation and training of the spared degrees of freedom after neural lesions, thus potentially bridging the gap between research and clinical application and advancing the development of intuitive EMG interfaces for diverse neural lesions., Comment: 23 pages, 8 figures

Computer programming initially required humans to directly translate their goals into machine code. These goals could have easily been expressed as a written (or human) language directive. Computers, however, had no capacity to satisfactorily interpret written language. Large language model's provide exactly this capability; automatic generation of computer programs or even assembly code from written language directives. This research examines dynamic code execution of written language directives within the context of a running application. It implements a text editor whose business logic is purely backed by large language model prompts. That is, the program's execution uses prompts and written language directives to dynamically generate application logic at the point in time it is needed. The research clearly shows how written language directives, backed by a large language model, offer radically new programming and operating system paradigms. For example, empowerment of users to directly implement requirements via written language directives, thus supplanting the need for a team ofprogrammers, a release schedule and the like. Or, new security mechanisms where static executables, always a target for reverse engineering or fuzzing, no longer exist. They are replaced by ephemeral executables that may continually change, be completely removed, and are easily updated., Comment: 6 pages, 4 figures

We study the formation and the subsequent dynamics of shock waves in repulsive one-dimensional Bose gases during the free expansion of a density hump. By building coherent Fermi states for interacting Bethe fermions, we define a quantum fluctuating initial state expressed in terms of universal quantities, namely the density and the Luttinger parameter. In the integrable case, this fluctuating state is then evolved by generalized hydrodynamics (GHD) and, differently from non-fluctuating initial states, it develops density ripples on top of the hydrodynamic mean value. Our analysis gives a general theory of quantum ripples and wave breaking in integrable and quasi-integrable one-dimensional liquids and clarifies the role of the interaction strength. In particular, for strongly/intermediately interacting bosons, we find quantum ripples originating from low-energy modes at the Fermi surface interfering when transported by GHD. In the low coupling limit, near the quasicondensate regime, we find instead that density ripples have a semi-classical nature, and their description requires information on the curvature of the Fermi surface., Comment: 19 pages, 7 figures

Epigenetic cell memory, the inheritance of gene expression patterns across subsequent cell divisions, is a critical property of multi-cellular organisms. In recent work [10], a subset of the authors observed in a simulation study how the stochastic dynamics and time-scale differences between establishment and erasure processes in chromatin modifications (such as histone modifications and DNA methylation) can have a critical effect on epigenetic cell memory. In this paper, we provide a mathematical framework to rigorously validate and extend beyond these computational findings. Viewing our stochastic model of a chromatin modification circuit as a singularly perturbed, finite state, continuous time Markov chain, we extend beyond existing theory in order to characterize the leading coefficients in the series expansions of stationary distributions and mean first passage times. In particular, we characterize the limiting stationary distribution in terms of a reduced Markov chain, provide an algorithm to determine the orders of the poles of mean first passage times, and determine how changing erasure rates affects system behavior. The theoretical tools developed in this paper not only allow us to set a rigorous mathematical basis for the computational findings of our prior work, highlighting the effect of chromatin modification dynamics on epigenetic cell memory, but they can also be applied to other singularly perturbed Markov chains beyond the applications in this paper, especially those associated with chemical reaction networks.

Interventions play a pivotal role in the study of complex biological systems. In drug discovery, genetic interventions (such as CRISPR base editing) have become central to both identifying potential therapeutic targets and understanding a drug's mechanism of action. With the advancement of CRISPR and the proliferation of genome-scale analyses such as transcriptomics, a new challenge is to navigate the vast combinatorial space of concurrent genetic interventions. Addressing this, our work concentrates on estimating the effects of pairwise genetic combinations on the cellular transcriptome. We introduce two novel contributions: Salt, a biologically-inspired baseline that posits the mostly additive nature of combination effects, and Peper, a deep learning model that extends Salt's additive assumption to achieve unprecedented accuracy. Our comprehensive comparison against existing state-of-the-art methods, grounded in diverse metrics, and our out-of-distribution analysis highlight the limitations of current models in realistic settings. This analysis underscores the necessity for improved modelling techniques and data acquisition strategies, paving the way for more effective exploration of genetic intervention effects.

In the context of epigenetic transformations in cancer metastasis, a puzzling effect was recently discovered, in which the elimination (knock-out) of an activating regulatory element leads to increased (rather than decreased) activity of the element being regulated. It has been postulated that this paradoxical behavior can be explained by activating and repressing transcription factors competing for binding to other possible targets. It is very difficult to prove this hypothesis in mammalian cells, due to the large number of potential players and the complexity of endogenous intracellular regulatory networks. Instead, this paper analyzes this issue through an analogous synthetic biology construct which aims to reproduce the paradoxical behavior using standard bacterial gene expression networks. The paper first reviews the motivating cancer biology work, and then describes a proposed synthetic construct. A mathematical model is formulated, and basic properties of uniqueness of steady states and convergence to equilibria are established, as well as an identification of parameter regimes which should lead to observing such paradoxical phenomena (more activator leads to less activity at steady state). A proof is also given to show that this is a steady-state property, and for initial transients the phenomenon will not be observed. This work adds to the general line of work of resource competition in synthetic circuits., Comment: 14 pages, 7 figures

The selective confinement of light holes (LHs) in a tensile-strained germanium (Ge) quantum well is studied by mapping the electronic structure of Ge$_{1-x}$Sn$_x$/Ge/Ge$_{1-x}$Sn$_x$ heterostructures as a function of Sn content, residual strain, and Ge well thickness. It is shown that above $12\,\text{at.}\%$ Sn and below $0.4\%$ residual compressive strain in the barriers, the tensile strain in Ge becomes sufficiently large to yield a valence band edge with LH-like character, thus forming a quasi two-dimensional LH gas in Ge. The LH ground state has a larger in-plane effective mass than that of heavy holes (HHs) in Si$_{1-y}$Ge$_y$/Ge/Si$_{1-y}$Ge$_y$ quantum wells. Moreover, LHs in optimal Ge$_{1-x}$Sn$_x$/Ge/Ge$_{1-x}$Sn$_x$ heterostructures are found to exhibit a strong $g$-tensor anisotropy, with the in-plane component one order of magnitude larger than that of HHs in typical planar systems. Two of three structure-inversion-asymmetry Rashba parameters, both of which are critical in electric-dipole-spin-resonance experiments, are effectively 10 times the size of the cubic Rashba parameter in HH quantum wells. In the regime of LH selective confinement, every layer of the heterostructure is of direct bandgap, which can be relevant for efficient optical photon-spin qubit interfaces. This work discusses the broad landscape of the characteristics of LH spin confined in Ge to guide the design and implementation of LH spin-based devices.

Two theorems with applications to the quantum theory of measurements are stated and proven. The first one clarifies and amends von Neumann's Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one clarifies the relationship between ``events'' and ``measurements'' and the meaning of measurements in the $ETH$-Approach to quantum mechanics., Comment: 14 pages, 0 figures, volume in memory of Giovanni Morchio, to be published by Springer-Nature in 2024

The set of states on ${\rm CCR}(\ch)$, the CCR algebra of a separable Hilbert space $\ch$, is here looked at as a natural object to obtain a non-commutative version of Freedman's theorem for unitarily invariant stochastic processes. In this regard, we provide a complete description of the compact convex set of states of ${\rm CCR}(\ch)$ that are invariant under the action of all automorphisms induced in second quantization by unitaries of $\ch$. We prove that this set is a Bauer simplex, whose extreme states are either the canonical trace of the CCR algebra or Gaussian states with variance at least $1$., Comment: 22 pages

We present the first exact theory and analytical formulas for the large-scale phase fluctuations in the sine-Gordon model, valid in all regimes of the field theory, for arbitrary temperatures and interaction strengths. Our result is based on the Ballistic Fluctuation Theory combined with Generalized Hydrodynamics, and can be seen as an exact ``dressing" of the phenomenological soliton-gas picture first introduced by Sachdev and Young [S. Sachdev and A. P. Young, PRL 78, 2220 (1997)], to the modes of Generalised Hydrodynamics. The resulting physics of phase fluctuations in the sine-Gordon model is qualitatively different, as the stable quasi-particles of integrability give coherent ballistic propagation instead of diffusive spreading. We provide extensive numerical checks of our analytical predictions within the classical regime of the field theory by using Monte Carlo methods. We discuss how our results are of ready applicability to experiments on tunnel-coupled quasicondensates., Comment: 8+14 pages; 4+2 Figures

Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and synthetic biology, but often have a large or infinite number of states, and thus are not amenable to computation and analysis. Due to this, approximations that rely on the molecular counts and the volume being large are commonly used, with the most common being the Reaction Rate Equations and the Linear Noise Approximation. For finite time intervals, Kurtz established the validity of the Reaction Rate Equations and Linear Noise Approximation, by proving law of large numbers and central limit theorem results respectively. However, the analogous question for the stationary distribution of the Markov chain model has remained mostly unanswered, except for chemical reaction networks with special structures or bounded molecular counts. In this work, we use Stein's Method to obtain sufficient conditions for the stationary distribution of an appropriately scaled Stochastic Chemical Reaction Network to converge to the Linear Noise Approximation as the system size goes to infinity. Our results give non asymptotic bounds on the error in the Reaction Rate Equations and in the Linear Noise Approximation as applied to the stationary distribution. As a special case, we give conditions under which the global exponential stability of an equilibrium point of the Reaction Rate Equations is sufficient to obtain our error bounds, thus permitting one to obtain conclusions about the Markov chain by analyzing the deterministic Reaction Rate Equations., Comment: 27 pages, 0 figures; Corrected typos and minor edits for clarity

It has recently become feasible to run personal digital assistants on phones and other personal devices. In this paper we describe a design for a natural language understanding system that runs on device. In comparison to a server-based assistant, this system is more private, more reliable, faster, more expressive, and more accurate. We describe what led to key choices about architecture and technologies. For example, some approaches in the dialog systems literature are difficult to maintain over time in a deployment setting. We hope that sharing learnings from our practical experiences may help inform future work in the research community.

In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie Schwinger block-diagonalization method} which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps. This improves earlier results concerning the persistence of the so called \emph{bulk} gap in these models, besides illustrating the power of our general methods in a non-trivial application.

The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of \emph{branch-point twist fields}, the starting point for computing R\'enyi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of R\'enyi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations., Comment: 53 pages, 2 figures