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The main purpose of this article is the study of an inverse problem for nonlocal porous medium equations (NPMEs) with a linear absorption term. More concretely, we show that under certain assumptions on the time-independent coefficients $\rho,q$ and the time-independent kernel $K$ of the nonlocal operator $L_K$, the (partial) Dirichlet-to-Neumann map uniquely determines the three quantities $(\rho,K,q)$ in the nonlocal porous medium equation $\rho \partial_tu+L_K(u^m)+qu=0$, where $m>1$. In the first part of this work we adapt the Galerkin method to prove existence and uniqueness of nonnegative, bounded solutions to the homogenoeus NPME with regular initial and exterior conditions. Additionally, a comparison principle for solutions of the NPME is proved, whenever they can be approximated by sufficiently regular functions like the one constructed for the homogeneous NPME. These results are then used in the second part to prove the unique determination of the coefficients $(\rho,K,q)$ in the inverse problem. Finally, we show that the assumptions on the nonlocal operator $L_K$ in our main theorem are satisfied by the fractional conductivity operator $\mathcal{L}_{\gamma}$, whose kernel is $\gamma^{1/2}(x)\gamma^{1/2}(y)/|x-y|^{n+2s}$ up to a normalization constant., Comment: 57 pages

We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equations. We do not assume that any solutions to these equations are known a priori, in which case the problem has a well known gauge symmetry. We determine, under additional assumptions, the semilinear term up to this symmetry in a time-dependent anisotropic case modeled on Riemannian manifolds, and for partial data measurements on $\mathbb{R}^n$. Moreover, we present cases where it is possible to exploit the nonlinear interaction to break the gauge symmetry. This leads to full determination results of the nonlinear term. As an application, we show that it is possible to give a full resolution to classes of inverse source problems of determining a source term and nonlinear terms simultaneously. This is in strict contrast to inverse source problems for corresponding linear equations, which always have the gauge symmetry. We also consider a Carleman estimate with boundary terms based on intrinsic properties of parabolic equations., 44 pages. All comments are welcome

We consider an inverse problem of determining the coefficients of a fractional $p\,$-Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction formula in the region where the exterior measurements are performed. This formula is then used to establish a global uniqueness result for real-analytic coefficents. In addition, we also derive a stability estimate for the unique determination of the coefficients in the exterior measurement set., 22 pages

This is the summary report of the Community Engagement Frontier for the Snowmass 2021 study of the future of particle physics. The report discusses a number of general issues of importance to the particle physics community, including (1) the relation of universities, national laboratories, and industry, (2) career paths for scientists engaged in particle physics, (3) diversity, equity, and inclusion, (4) physics education, (5) public education and outreach, (6) engagement with the government and public policy, and (7) the environmental and social impacts of particle physics., 51 pages, 2 figures; to appear in the proceedings of the 2021 Community Study on the Future of U.S. Particle Physics (Snowmass 2021)

We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the partial exterior Dirichlet-to-Neumann map locally determines the diffusion coefficient in the exterior domain. In addition, we introduce a novel analysis of nonlocal Neumann derivatives to prove an interior determination result. Interior and exterior determination yield the desired global uniqueness theorem for the Calder\'on problem of nonlocal diffusion equations with time-dependent coefficients. This work extends recent studies from nonlocal elliptic equations with global coefficients to their parabolic counterparts. The results hold for any spatial dimension $n\geq 1$., Comment: 37 pages

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder\'on problems, respectively., Comment: 34 pages. All comments are welcome. Several typos are corrected

In collaboration with the American College of Veterinary Radiology

We study inverse source problems associated to semilinear elliptic equations of the form \[ \Delta u(x)+a(x,u)=F(x), \] on a bounded domain $\Omega\subset \mathbb{R}^n$, $n\geq 2$. We show that it is possible to use nonlinearity to break the gauge symmetry of the inverse source problem for a class of nonlinearities $a(x,u)$. This is in contrast to inverse source problems for linear equations, which always have a gauge symmetry. The class of nonlinearities include certain polynomials and exponential nonlinearities. For these nonlinearities, we determine both $a(x,u)$ and $F(x)$ uniquely from the associated DN map. Moreover, for general nonlinearities $a(x,u)$, we show that we can recover the derivatives $\partial_u^ka(x,u)$ and the source $F(x)$ up to a gauge. Especially, we recover general polynomial nonlinearities up to a gauge and generalize results of [FO20,LLLS20] by removing the assumption that $u\equiv 0$ is a solution., Comment: 27 pages. All comments are welcome

An e-book system allows students to access learning materials regardless of location or time. However, reading e-books without additional guidance could be inefficient for students and thereby affecting their learning engagement and learning outcomes. In this study, a learning analytics-based (LA) e-learning approach was proposed to resolve the situation. Moreover, experimental design methods were used to explore the relationship between the learning engagement, behavior, and achievement of students who learned with the LA e-learning approach. The research results show that the learning performance of high- engagement participants using the LA e-learning approach is better than that of low- engagement participants. In addition, the findings indicated that the proposed method could support low and medium learners to improve their learning achievement. These findings could be a valuable reference for those who intend to develop an effective learning analytics-based learning approach through e-book systems., 28th International Conference on Computers in Education, 23-27 November 2020, Web conference.

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calderón problems, respectively., 34 pages. All comments are welcome. Several typos are corrected

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determinination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined., Comment: 46 pages, 10 figures, 105 references, with hyperlinks to relevant computer codes and related information; Figure 8 in version 2 corrected; accepted for publication in "Methods in Molecular Biology" volume "Phase-Separated Biomolecular Condensates" edited by H.-X. Zhou, J.-H. Spille, and P. Banerjee (expected October 2022)

We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the partial exterior Dirichlet-to-Neumann map locally determines the diffusion coefficient in the exterior domain. In addition, we introduce a novel analysis of nonlocal Neumann derivatives to prove an interior determination result. Interior and exterior determination yield the desired global uniqueness theorem for the Calderón problem of nonlocal diffusion equations with time-dependent coefficients. This work extends recent studies from nonlocal elliptic equations with global coefficients to their parabolic counterparts. The results hold for any spatial dimension $n\geq 1$., 37 pages

In this paper, we study several inverse problems associated with a fractional differential equation of the following form: \[ (-\Delta)^s u(x)+\sum_{k=0}^N a^{(k)}(x) [u(x)]^k=0,\ \ 0, Comment: 24 page. All comments are welcome. There are few typos corrected in V2

Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined from the knowledge of the Dirichlet-to-Neumann map associated to the semilinear elliptic equation. This extends the previously known results of the works [FO20, LLLS21a]. Our proof is based on analyzing higher order linearizations of the semilinear equation with non-vanishing boundary traces and also the study of interactions of two or more products of the so-called Gaussian quasimode solutions to the linearized equation., Comment: 39 pages. All comments are welcome

There are hundreds of RNA binding proteins in the human genome alone and their interactions with messenger and other RNAs in a cell regulate every step in an RNA's life cycle. To understand this interplay of proteins and RNA it is important to be able to know which protein binds which RNA how strongly and where. Here, we introduce RBPBind, a web-based tool for the quantitative prediction of the interaction of single-stranded RNA binding proteins with target RNAs that fully takes into account the effect of RNA secondary structure on binding affinity. Given a user-specified RNA and a protein selected from a set of several RNA-binding proteins, RBPBind computes their binding curve and effective binding constant. The server also computes the probability that, at a given protein concentration, a protein molecule will bind to any particular nucleotide along the RNA. The sequence specificity of the protein-RNA interaction is parameterized from public RNAcompete experiments and integrated into the recursions of the Vienna RNA package to simultaneously take into account protein binding and RNA secondary structure. We validate our approach by comparison to experimentally determined binding affinities of the HuR protein for several RNAs of different sequence contexts from the literature, showing that integration of raw sequence affinities into RNA secondary structure prediction significantly improves the agreement between computationally predicted and experimentally measured binding affinities. Our resource thus provides a quick and easy way to obtain reliable predicted binding affinities and locations for single-stranded RNA binding proteins based on RNA sequence alone.

We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic scenarios that one can uniquely determine the nonlinearity or the sources by using passive or active boundary observations. In order to exploit the nonlinearity and the sources simultaneously, we develop a new technique, which combines the observability for linear wave equations and a Runge approximation with higher order linearization for the semilinear hyperbolic equation., Comment: 31 pages. Some typos are corrected. All comments are welcome

In random expected utility (Gul and Pesendorfer, 2006), the distribution of preferences is uniquely recoverable from random choice. This paper shows through two examples that such uniqueness fails in general if risk preferences are random but do not conform to expected utility theory. In the first, non-uniqueness obtains even if all preferences are confined to the betweenness class (Dekel, 1986) and are suitably monotone. The second example illustrates random choice behavior consistent with random expected utility that is also consistent with random non-expected utility. On the other hand, we find that if risk preferences conform to weighted utility theory (Chew, 1983) and are monotone in first-order stochastic dominance, random choice again uniquely identifies the distribution of preferences. Finally, we argue that, depending on the domain of risk preferences, uniqueness may be restored if joint distributions of choice across a limited number of feasible sets are available.

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS), we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess the roles of electrostatic, hydrophobic, cation-$��$, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated 3 residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-$��$ interactions consistently accounted for the experimental LLPS data on the wildtype, a charge-scrambled, an FtoA, and an RtoK mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and LLPS experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, the important LLPS-driving $��$-related interactions are embodied in classical statistical potentials. Further elucidation will be necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and YtoF mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than those posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which depends on protein concentration. Analytical theory suggests that this dependence entails enhanced inter-protein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to a modest overall impact on LLPS., 65 pages (main text and supporting information), 7 main-text figures, 7 supporting figures, 1 supporting table, 135 references; accepted for publication in the Proceedings of the National Academy of Sciences, U.S.A

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0, Comment: 34 pages

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these two systems from the corresponding boundary measurements. In a first step we reconstruct Lipschitz magnetic permeability, electric permittivity and conductivity on the surface from the ideal boundary measurements. Then, we study inverse problems for Maxwell equations and the isotropic elasticity system assuming that the data contains measurement errors. For both systems, we provide explicit formulas to reconstruct the parameters on the boundary as well as its rate of convergence formula., Comment: 25 pages

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam�� moduli for these two systems from the corresponding boundary measurements. In a first step we reconstruct Lipschitz magnetic permeability, electric permittivity and conductivity on the surface from the ideal boundary measurements. Then, we study inverse problems for Maxwell equations and the isotropic elasticity system assuming that the data contains measurement errors. For both systems, we provide explicit formulas to reconstruct the parameters on the boundary as well as its rate of convergence formula., 25 pages

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-��)^s+Q$ with $0, 34 pages

In this work, we use monotonicity-based methods for the fractional Schr��dinger equation with general potentials $q\in L^\infty(��)$ in a Lipschitz bounded open set $��\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder��n problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Schr��dinger equation, and we prove uniqueness and Lipschitz stability from finitely many measurements for potentials lying in an a-priori known bounded set in a finite dimensional subset of $L^\infty(��)$.

Let $\mathcal Q_D$ be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order $\mathcal O$ in an indefinite quaternion algebra of discriminant $D$ over $\mathbb Q$ such that the Rosati involution coincides with a positive involution of the form $\alpha\mapsto\mu^{-1}\overline\alpha\mu$ on $\mathcal O$ for some $\mu\in\mathcal O$ with $\mu^2+D=0$. In this paper, we first give a formula for the number of irreducible components in $\mathcal Q_D$, strengthening an earlier result of Rotger. Then for each irreducible component of genus $0$, we determine its rational parameterization in terms of a Hauptmodul of the associated Shimura curve., Comment: 40 pages, plus 70+ pages of tables

An observation of neutrinoless double beta decay, a hypothetical second-order weak interaction, may reveal the Dirac/Majorana nature of the neutrinos and demonstrate lepton number violation. The EXO-200 experiment was designed to search for neutrinoless double beta decay using an ultra-low background single-phase time projection chamber. The detector contains 110~kg of active liquid xenon, isotopically enriched in Xe-136, which acts as both the decaying nucleus and detection medium. To optimize the signal of such a detector, the liquid xenon needs to be kept free of electronegative impurities which could interact with drifting electron signals and reduce energy resolution. This study investigates whether fitting the ionization signals from the two time projection chamber halves separately or combining the datasets for fitting yields a more accurate purity correction. The latter method was found to improve the purity correction on the EXO-200 data and has been implemented in the EXO-200 standard analysis pipeline. Using the combined dataset, a purification model and its modifications have been developed and tested. The purification model utilizes the physical parameters measured in the detector and can improve the understanding of purity behavior in the detector, while providing detector measurements. The fitting performance of the 2-Phase Model to EXO-200 electron lifetime data is shown to be comparable to that of the polynomial function method. In addition, the 2-Phase Model can adapt to changes in the system and does not require human input, thus eliminating any inconsistency in the purity correction for the ionization energy in the physics data.

We investigate the Calder��n problem for the fractional Schr��dinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does \emph{not} enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many \emph{generic} measurements is discussed. Here the genericity is obtained through \emph{singularity theory} which might also be interesting in the context of hybrid inverse problems. Combined with the results from \cite{GRSU18}, this yields a finite measurements constructive reconstruction algorithm for the fractional Calder��n problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension $n\geq 1$., 42 pages, this is an extended version of v1 in which we have expanded the reconstruction part. In particular, we have added a section on the genericity of certain nonlinear constraints

We study global uniqueness in an inverse problem for the fractional semilinear Schr\"{o}dinger equation $(-\Delta)^{s}u+q(x,u)=0$ with $s\in (0,1)$. We show that an unknown function $q(x,u)$ can be uniquely determined by the Cauchy data set. In particular, this result holds for any space dimension greater than or equal to $2$. Moreover, we demonstrate the comparison principle and provide a $L^\infty$ estimate for this nonlocal equation under appropriate regularity assumptions.

In this paper, we introduce an inverse problem of a Schr\"odinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0, Comment: 41 pages

We study global uniqueness in an inverse problem for the fractional semilinear Schr��dinger equation $(-��)^{s}u+q(x,u)=0$ with $s\in (0,1)$. We show that an unknown function $q(x,u)$ can be uniquely determined by the Cauchy data set. In particular, this result holds for any space dimension greater than or equal to $2$. Moreover, we demonstrate the comparison principle and provide a $L^\infty$ estimate for this nonlocal equation under appropriate regularity assumptions.

In this paper, we introduce an inverse problem of a Schr��dinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0, 41 pages

We consider the inverse problems of for the fractional Schr��dinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calder��n problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension $n\geq 2$ and only requires the background solution of the fractional Schr��dinger equation.

Let $A\in\mathrm{Sym}(n\times n)$ be an elliptic 2-tensor. Consider the anisotropic fractional Schr��dinger operator $\mathscr{L}_A^s+q$, where $\mathscr{L}_A^s:=(-\nabla\cdot(A(x)\nabla))^s$, $s\in (0, 1)$ and $q\in L^\infty$. We are concerned with the simultaneous recovery of $q$ and possibly embedded soft or hard obstacles inside $q$ by the exterior Dirichlet-to-Neumann (DtN) map outside a bounded domain $��$ associated with $\mathscr{L}_A^s+q$. It is shown that a single measurement can uniquely determine the embedded obstacle, independent of the surrounding potential $q$. If multiple measurements are allowed, then the surrounding potential $q$ can also be uniquely recovered. These are surprising findings since in the local case, namely $s=1$, both the obstacle recovery by a single measurement and the simultaneous recovery of the surrounding potential by multiple measurements are longstanding problems and still remain open in the literature. Our argument for the nonlocal inverse problem is mainly based on the strong uniqueness property and Runge approximation property for anisotropic fractional Schr��dinger operators.

We consider the inverse boundary value problem of determining the Lam�� moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity assumptions as weak as possible on the Lam�� moduli and on the boundary, we give explicit pointwise reconstruction formulae of the Lam�� moduli and their higher order derivatives at the boundary from the localized Dirichlet-to-Neumann map., 24 pages

The nearly cloaking via transformation optics approach for the isotropic elastic wave fields is considered. This work extends the study of the nearly cloaking scheme to the elasticity system with residual stress in \mathbb{R}^{N} for N=2,3, which is an anisotropic elasticity system. It is worth to mention that there are no minor symmetric properties for the elastic tensor with residual stress and this system is invariant under a coordinate transformation. Therefore, we think the elasticity system residual stress model is more natural than the isotropic elasticity system in designing the elastic cloaking medium in the physical sense. In addition, the main difficulty of treating this problem lies in the fact that there are no layer potential theory for the residual stress system. Instead, we will derive suitable elliptic estimates for the elasticity system residual stress by comparing with the Lam\'e system to achieve desired results.

Yi-Hsuan Lin Abstract in engl. sprache Linz, Univ., Master-Arb., 2015

Breast cancer is the most frequently diagnosed cancer among Canadian women. Despite the use of advanced therapeutics, breast cancer remains the second leading cause of cancer death among Canadian women. Therefore, the development of novel and effective therapeutics to treat breast cancer remains an important goal. Defective or inhibited apoptosis is a major causative factor in the development and progression of cancer. Zinc is considered an apoptotic regulator. Further, previous work has also shown that there is an association between zinc depletion-induced apoptosis and an elevated intracellular Ca²⁺ level in human breast cancer MDA-MB-231 cells. Ca²⁺ is a known mediator of the mitochondrial apoptotic pathway. The overall objective of my thesis research was to investigate the role of intracellular Ca²⁺ and its involvement of the mitochondria in zinc depletion-induced apoptosis in human breast cancer MDA-MB-231 cells. MDA-MB-231 cells were cultured in DMEM containing FBS (10%) followed by depletion of intracellular zinc using N,N,N’,N’-tetrakis (2-pyridylmethyl) ethylenediamine (TPEN; 20 µM) with or without the presence of intracellular Ca²⁺ chelator, 1,2-bis (2-aminophenoxy) ethane-N,N,N’,N’-tetraacetic acid acetoxymethyl ester (BAPTA-AM; 10 or 20 µM). Apoptosis was assessed by caspase-9 and -3 activities using corresponding fluorogenic substrates and the proportion of cells with fragmented DNA using PI-staining flow cytometry assay. Intracellular Ca²⁺ was assessed using Fura-2 assay. Mitochondrial membrane potential was assessed by DiOC₆-staining flow cytometry assay. Cytochrome c release was detected by Western blot. Addition of TPEN resulted in an increase of caspase-9 and -3 activities, an increase in the proportion of cells with fragmented DNA, and a prolonged increase in intracellular Ca²⁺ level. TPEN treatment also reduced mitochondrial membrane potential and induced cytochrome c release. Zinc replenishment (10 – 40 µM) prevented TPEN-induced apoptosis. Intracellular Ca²⁺ chelation with BAPTA-AM suppressed TPEN-induced apoptosis, mitochondrial membrane potential loss, and cytochrome c release. Collectively these results showed that zinc depletion-induced apoptosis was mediated through the Ca²⁺-dependent mitochondrial apoptotic pathway in human breast cancer MDA-MB-231 cells.

Biomolecular condensates consisting of proteins and nucleic acids can serve critical biological functions, so that some condensates are referred as membraneless organelles. They can also be disease‐causing, if their assembly is misregulated. A major physicochemical basis of the formation of biomolecular condensates is liquid–liquid phase separation (LLPS). In general, LLPS depends on environmental variables, such as temperature and hydrostatic pressure. The effects of pressure on the LLPS of a binary SynGAP/PSD‐95 protein system mimicking postsynaptic densities, which are protein assemblies underneath the plasma membrane of excitatory synapses, were investigated. Quite unexpectedly, the model system LLPS is much more sensitive to pressure than the folded states of typical globular proteins. Phase‐separated droplets of SynGAP/PSD‐95 were found to dissolve into a homogeneous solution already at ten‐to‐hundred bar levels. The pressure sensitivity of SynGAP/PSD‐95 is seen here as a consequence of both pressure‐dependent multivalent interaction strength and void volume effects. Considering that organisms in the deep sea are under pressures up to about 1 kbar, this implies that deep‐sea organisms have to devise means to counteract this high pressure sensitivity of biomolecular condensates to avoid harm. Intriguingly, these findings may shed light on the biophysical underpinning of pressure‐related neurological disorders in terrestrial vertebrates., High pressure sensitivity of postsynaptic densities: Quite unexpectedly, a binary protein condensate mimicking postsynaptic densities, which are protein assemblies underneath the plasma membrane of excitatory synapses, reveals high pressure sensitivity, which may shed light on the biophysical underpinnings of pressure‐related neurological disorders.