Robustness in projected entangled pair states

We analyze a criterion which guarantees that the ground states of certain many-body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restricted version of the local topological quantum order (LTQO) condition [Michalakis and Pytel, Commun. Math. Phys. 322, 277 (2013)] provides a checkable criterion which allows us to assess the stability of local properties of PEPS under physical perturbations. We moreover show that LTQO itself is stable under perturbations which preserve the spectral gap, leading to nontrivial examples of PEPS which possess LTQO and are thus stable under arbitrary perturbations

Elementary Excitations in Gapped Quantum Spin Systems

For quantum lattice systems with local interactions, the Lieb-Robinson bound serves as an alternative for the strict causality of relativistic systems and allows the proof of many interesting results, in particular, when the energy spectrum exhibits an energy gap. In this Letter, we show that for translation invariant systems, simultaneous eigenstates of energy and momentum with an eigenvalue that is separated from the rest of the spectrum in that momentum sector can be arbitrarily well approximated by building a momentum superposition of a local operator acting on the ground state. The error satisfies an exponential bound in the size of the support of the local operator, with a rate determined by the gap below and above the targeted eigenvalue. We show this explicitly for the Affleck-Kennedy-Lieb-Tasaki model and discuss generalizations and applications of our result

Morpho-Rheological Fingerprinting of Rod Photoreceptors Using Real-Time Deformability Cytometry

Distinct cell-types within the retina are mainly specified by morphological and molecular parameters, however, physical properties are increasingly recognized as a valuable tool to characterize and distinguish cells in diverse tissues. High-throughput analysis of morpho-rheological features has recently been introduced using real-time deformability cytometry (RT-DC) providing new insights into the properties of different cell-types. Rod photoreceptors represent the main light sensing cells in the mouse retina that during development forms apically the densely packed outer nuclear layer. Currently, enrichment and isolation of photoreceptors from retinal primary tissue or pluripotent stem cell-derived organoids for analysis, molecular profiling, or transplantation is achieved using flow cytometry or magnetic activated cell sorting approaches. However, such purification methods require genetic modification or identification of cell surface binding antibody panels. Using primary retina and embryonic stem cell-derived retinal organoids, we characterized the inherent morpho-mechanical properties of mouse rod photoreceptors during development based on RT-DC. We demonstrate that rods become smaller and more compliant throughout development and that these features are suitable to distinguish rods within heterogenous retinal tissues. Hence, physical properties should be considered as additional factors that might affect photoreceptor differentiation and retinal development besides representing potential parameters for label-free sorting of photoreceptors

Contribution of the cyclic nucleotide gated channel subunit, CNG-3, to olfactory plasticity in Caenorhabditis elegans.

In Caenorhabditis elegans, the AWC neurons are thought to deploy a cGMP signaling cascade in the detection of and response to AWC sensed odors. Prolonged exposure to an AWC sensed odor in the absence of food leads to reversible decreases in the animal's attraction to that odor. This adaptation exhibits two stages referred to as short-term and long-term adaptation. Previously, the protein kinase G (PKG), EGL-4/PKG-1, was shown necessary for both stages of adaptation and phosphorylation of its target, the beta-type cyclic nucleotide gated (CNG) channel subunit, TAX-2, was implicated in the short term stage. Here we uncover a novel role for the CNG channel subunit, CNG-3, in short term adaptation. We demonstrate that CNG-3 is required in the AWC for adaptation to short (thirty minute) exposures of odor, and contains a candidate PKG phosphorylation site required to tune odor sensitivity. We also provide in vivo data suggesting that CNG-3 forms a complex with both TAX-2 and TAX-4 CNG channel subunits in AWC. Finally, we examine the physiology of different CNG channel subunit combinations

Long-term and age-dependent restoration of visual function in a mouse model of CNGB3-associated achromatopsia following gene therapy

Mutations in the CNGB3 gene account for >50% of all known cases of achromatopsia. Although of early onset, its stationary character and the potential for rapid assessment of restoration of retinal function following therapy renders achromatopsia a very attractive candidate for gene therapy. Here we tested the efficacy of an rAAV2/8 vector containing a human cone arrestin promoter and a human CNGB3 cDNA in CNGB3 deficient mice. Following subretinal delivery of the vector, CNGB3 was detected in both M- and S-cones and resulted in increased levels of CNGA3, increased cone density and survival, improved cone outer segment structure and normal subcellular compartmentalization of cone opsins. Therapy also resulted in long-term improvement of retinal function, with restoration of cone ERG amplitudes of up to 90% of wild-type and a significant improvement in visual acuity. Remarkably, successful restoration of cone function was observed even when treatment was initiated at 6 months of age; however, restoration of normal visual acuity was only possible in younger animals (e.g. 2–4 weeks old). This study represents achievement of the most substantial restoration of visual function reported to date in an animal model of achromatopsia using a human gene construct, which has the potential to be utilized in clinical trials

Pathological and ecological host consequences of infection by an introduced fish parasite

The infection consequences of the introduced cestode fish parasite Bothriocephalus acheilognathi were studied in a cohort of wild, young-of-the-year common carp Cyprinus carpio that lacked co-evolution with the parasite. Within the cohort, parasite prevalence was 42% and parasite burdens were up to 12% body weight. Pathological changes within the intestinal tract of parasitized carp included distension of the gut wall, epithelial compression and degeneration, pressure necrosis and varied inflammatory changes. These were most pronounced in regions containing the largest proportion of mature proglottids. Although the body lengths of parasitized and non-parasitized fish were not significantly different, parasitized fish were of lower body condition and reduced weight compared to non-parasitized conspecifics. Stable isotope analysis (δ15N and δ13C) revealed trophic impacts associated with infection, particularly for δ15N where values for parasitized fish were significantly reduced as their parasite burden increased. In a controlled aquarium environment where the fish were fed ad libitum on an identical food source, there was no significant difference in values of δ15N and δ13C between parasitized and non-parasitized fish. The growth consequences remained, however, with parasitized fish growing significantly slower than non-parasitized fish, with their feeding rate (items s−1) also significantly lower. Thus, infection by an introduced parasite had multiple pathological, ecological and trophic impacts on a host with no experience of the parasite

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an $s$-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the {\em spectral flow}, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models $H(s), 0\leq s\leq 1$.Comment: Updated acknowledgments and new email address of S

Presynaptic partner selection during retinal circuit reassembly varies with timing of neuronal regeneration in vivo

Whether neurons can restore their original connectivity patterns during circuit repair is unclear. Taking advantage of the regenerative capacity of zebrafish retina, we show here the remarkable specificity by which surviving neurons reassemble their connectivity upon regeneration of their major input. H3 horizontal cells (HCs) normally avoid red and green cones, and prefer ultraviolet over blue cones. Upon ablation of the major (ultraviolet) input, H3 HCs do not immediately increase connectivity with other cone types. Instead, H3 dendrites retract and re-extend to contact new ultraviolet cones. But, if regeneration is delayed or absent, blue-cone synaptogenesis increases and ectopic synapses are made with red and green cones. Thus, cues directing synapse specificity can be maintained following input loss, but only within a limited time period. Further, we postulate that signals from the major input that shape the H3 HC's wiring pattern during development persist to restrict miswiring after damage

Genetic signs of multiple colonization events in Baltic ciscoes with radiation into sympatric spring- and autumn-spawners confined to early postglacial arrival

Presence of sympatric populations may reflect local diversification or secondary contact of already distinct forms. The Baltic cisco (Coregonus albula) normally spawns in late autumn, but in a few lakes in Northern Europe sympatric autumn and spring- or winter-spawners have been described. So far, the evolutionary relationships and taxonomic status of these main life history forms have remained largely unclear. With microsatellites and mtDNA sequences, we analyzed extant and extinct spring- and autumn-spawners from a total of 23 Swedish localities, including sympatric populations. Published sequences from Baltic ciscoes in Germany and Finland, and Coregonus sardinella from North America were also included together with novel mtDNA sequences from Siberian C.sardinella. A clear genetic structure within Sweden was found that included two population assemblages markedly differentiated at microsatellites and apparently fixed for mtDNA haplotypes from two distinct clades. All sympatric Swedish populations belonged to the same assemblage, suggesting parallel evolution of spring-spawning rather than secondary contact. The pattern observed further suggests that postglacial immigration to Northern Europe occurred from at least two different refugia. Previous results showing that mtDNA in Baltic cisco is paraphyletic with respect to North American C.sardinella were confirmed. However, the inclusion of Siberian C.sardinella revealed a more complicated pattern, as these novel haplotypes were found within one of the two main C.albula clades and were clearly distinct from those in North American C.sardinella. The evolutionary history of Northern Hemisphere ciscoes thus seems to be more complex than previously recognized

Fitness Ranking of Individual Mutants Drives Patterns of Epistatic Interactions in HIV-1

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