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Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravity. Moreover, in the frames of our model, we obtain that the laws of Non-relativistic Quantum Mechanics also invariant under the change of inertial or non-inertial cartesian coordinate system. Comment: Section about Maxwell Equations in Dielectric/Magnetic mediums was modified and improved, subsequent sections modified correspondingly

Current spacecraft mass are mostly fuel, this is dictated by the lack of fueling stations in space and also by the Tsiolkovsky rocket equation which defines the mass ratio needed to escape earths gravity. The Tsiolkovsky rocket equation gives a relationship between the mass ratio and the final velocity in multiples of the exhaust speed, and dictates a high mass ratio for current exhaust speeds. A relativistic motor exchanging momentum and energy with the electromagnetic field may mitigate such considerations, enabling efficient interplanetary travel. In this paper we will discuss the advantages and challenges of this novel mover for space transportation. Comment: 19 pages, 9 figures

Abstract Atomically-precise engineering of defects in topological quantum materials, which is essential for constructing new artificial quantum materials with exotic properties and appealing for practical quantum applications, remains challenging due to the hindrances in modifying complex lattice with atomic precision. Here, we report the atomically-precise engineering of the vacancy-localized spin-orbital polarons (SOP) in a kagome magnetic Weyl semimetal Co3Sn2S2, using scanning tunneling microscope. We achieve the repairing of the selected single vacancy and create atomically-precise sulfur quantum antidots with elaborate geometry through vacancy-by-vacancy repairing. We find that that the bound states of SOP experience a symmetry-dependent energy shift towards Fermi level with increasing vacancy size driven by the anti-bond interactions. Strikingly, as vacancy size increases, the localized magnetic moments of SOPs are tunable and ultimately extended to the negative magnetic moments resulting from spin-orbit coupling in the kagome flat band. These findings establish a new platform for engineering atomic quantum states in topological quantum materials, offering potential for kagome-lattice-based spintronics and quantum technologies.

Abstract This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step approach. In Step 1, a three-dimensional model based on generalized logarithmic spirals is used with heuristics in combination with a gradient-based solver to perform an automated multi-objective global search of trajectories and optimize for parameters defining the spirals, the launch date, as well as the number, sequence and configuration of the planetary flybys. In Step 2, candidate solutions from Step 1 are refined by further optimization with a direct method. Results show that, compared to similar algorithms based on two-dimensional models, the strategy implemented in Step 1 leads to better estimates of the optimal trajectories, especially when the orbits of the involved bodies are inclined with respect to the ecliptic plane. The proposed approximate method (Step 1) yields better agreement with high-fidelity solutions (Step 2) in terms of launch, flyby and arrival dates, in-plane and out-of-plane average LT accelerations and propellant consumption, leading to improved convergence when the Step 1 trajectories are employed to initiate the search in Step 2.

Life is homochiral and homochirality is a fundamental feature of living systems on Earth. While the exact mechanism that led to homochirality is still not fully understood, any realistic scenario on the origins of life needs to address the emergence of homochirality. In order to impose and maintain chirality in a prebiotic network, an environmental factor functioning as a chiral agent is demanded. Magnetized surfaces are prebiotically plausible chiral agents, shown to be effective in enantioseparation of ribose-aminooxazoline (RAO), a ribonucleic acid (RNA) precursor, due to the chiral-induced spin selectivity (CISS) effect. As such, mechanisms for breaking the magnetic symmetry of magnetic minerals are of the utmost importance. Here we report the avalanche magnetization of magnetite $(Fe_{3}O_{4})$ by the crystallization of enantiopure RAO. The observed breaking of the magnetic symmetry is induced by the chiral molecules due to the CISS effect and spreads out across the magnetic surface like an avalanche, providing a way to uniformly magnetize a magnetic surface without fully covering it. Considered together with our previous results on enantioseparation by crystallization on a magnetic surface, chirality-induced avalanche magnetization paves the way for a cooperative feedback between chiral molecules and magnetic surfaces. With this feedback, a weak natural bias in the net magnetization can be amplified and spin-selective processes can be accommodated on magnetic minerals on a persistent basis. Comment: 19 pages, 6 figures

Abstract Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same vertex set, called layers and aim to transform all layers into cluster graphs (disjoint unions of cliques) that differ only slightly. More specifically, we want to mark at most d vertices and to transform each layer into a cluster graph using at most k edge additions or deletions per layer so that, if we remove the marked vertices, we obtain the same cluster graph in all layers. In Temporal Cluster Editing we receive a sequence of layers and we want to transform each layer into a cluster graph so that consecutive layers differ only slightly. That is, we want to transform each layer into a cluster graph with at most k edge additions or deletions and to mark a distinct set of d vertices in each layer so that each two consecutive layers are the same after removing the vertices marked in the first of the two layers. We study the combinatorial structure of the two problems via their parameterized complexity with respect to the parameters d and k, among others. Despite the similar definition, the two problems behave quite differently: In particular, Multi-Layer Cluster Editing is fixed-parameter tractable with running time kO(k+d) sO(1) for inputs of size s, whereas Temporal Cluster Editing is W[1]-hard with respect to k even if d = 3.

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) in Euclidean and general $\ell_p^d$ spaces. Specifically, we focus on three settings that are still far from well understood: (1) DP-SCO over a constrained and bounded (convex) set in Euclidean space; (2) unconstrained DP-SCO in $\ell_p^d$ space; (3) DP-SCO with heavy-tailed data over a constrained and bounded set in $\ell_p^d$ space. For problem (1), for both convex and strongly convex loss functions, we propose methods whose outputs could achieve (expected) excess population risks that are only dependent on the Gaussian width of the constraint set rather than the dimension of the space. Moreover, we also show the bound for strongly convex functions is optimal up to a logarithmic factor. For problems (2) and (3), we propose several novel algorithms and provide the first theoretical results for both cases when $1

We consider a model of Parisi where a single particle hops on an infinite-dimensional hypercube, under the influence of a uniform but disordered magnetic flux. We reinterpret the hypercube as the Fock-space graph of a many-body Hamiltonian, and the flux as a frustration of the return amplitudes in Fock space. We will show that this model has the same correlation functions as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model, and hence is an equally good quantum model for near-AdS$_2$/near-CFT$_{1}$ (NAdS$_2$/NCFT$_1$) holography. Unlike the SYK model, the hypercube Hamiltonian is not $p$-local. Instead, the SYK model can be understood as a Fock-space model with similar frustrations. Hence we propose this type of Fock-space frustration as the broader characterization for NAdS$_2$/NCFT$_1$ microscopics, and speculate the possible origin of such frustrations.

The interactions between cells and the extracellular matrix are vital for the self-organisation of tissues. In this paper we present proof-of-concept to use machine learning tools to predict the role of this mechanobiology in the self-organisation of cell-laden hydrogels grown in tethered moulds. We develop a process for the automated generation of mould designs with and without key symmetries. We create a large training set with $N=6500$ cases by running detailed biophysical simulations of cell-matrix interactions using the contractile network dipole orientation (CONDOR) model for the self-organisation of cellular hydrogels within these moulds. These are used to train an implementation of the \texttt{pix2pix} deep learning model, reserving $740$ cases that were unseen in the training of the neural network for training and validation. Comparison between the predictions of the machine learning technique and the reserved predictions from the biophysical algorithm show that the machine learning algorithm makes excellent predictions. The machine learning algorithm is significantly faster than the biophysical method, opening the possibility of very high throughput rational design of moulds for pharmaceutical testing, regenerative medicine and fundamental studies of biology. Future extensions for scaffolds and 3D bioprinting will open additional applications. Comment: 26 Pages, 11 Figures

Over the past few years, wide-field time-domain surveys like ZTF and OGLE have led to discoveries of various types of interesting short-period stellar variables, such as ultracompact eclipsing binary white dwarfs, rapidly rotating magnetised white dwarfs (WDs), transitional cataclysmic variables between hydrogen-rich and helium accretion, and blue large-amplitude pulsators (BLAPs), which greatly enrich our understandings of stellar physics under some extreme conditions. In this paper, we report the first-two-year discoveries of short-period variables (i.e., P<2 hr) by the Tsinghua University-Ma Huateng Telescopes for Survey (TMTS). TMTS is a multi-tube telescope system with a field of view up to 18 deg^2, which started to monitor the LAMOST sky areas since 2020 and generated uninterrupted minute-cadence light curves for about ten million sources within 2 years. Adopting the Lomb-Scargle periodogram with period-dependent thresholds for the maximum powers, we identify over 1 100 sources that exhibit a variation period shorter than 2 hr. Compiling the light curves with the Gaia magnitudes and colours, LAMOST spectral parameters, VSX classifications, and archived observations from other prevailing time-domain survey missions, we identified 1 076 as delta Scuti stars, which allows us study their populations and physical properties in the short-period regime. The other 31 sources include BLAPs, subdwarf B variables (sdBVs), pulsating WDs, ultracompact/short-period eclipsing/ellipsoidal binaries, cataclysmic variables below the period gap, etc., which are highly interesting and worthy of follow-up investigations. Comment: 22 pages, 15 figures, 5 tables, accepted by MNRAS