Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions

We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology. A central benefit of our construction is that it produces an explicit finite-depth quantum circuit (FDQC) that prepares the ground state from an unentangled symmetric state. The FDQC allows us to clearly demonstrate the characteristic properties of supercohomology phases—namely, symmetry fractionalization on fermion parity flux loops—predicted by continuum formulations. By composing the corresponding FDQCs, we also recover the stacking relations of supercohomology phases. Furthermore, we derive topologically ordered gapped boundaries for the supercohomology models by extending the protecting symmetries, analogous to the construction of topologically ordered boundaries for bosonic SPT phases. Our approach relies heavily on dualities that relate certain bosonic 2-group SPT phases with supercohomology SPT phases. We develop physical motivation for the dualities in terms of explicit lattice prescriptions for gauging a 1-form symmetry and for condensing emergent fermions. We also comment on generalizations to supercohomology phases in higher dimensions and to fermionic SPT phases outside of the supercohomology framework

Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions

We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology. A central benefit of our construction is that it produces an explicit finite-depth quantum circuit (FDQC) that prepares the ground state from an unentangled symmetric state. The FDQC allows us to clearly demonstrate the characteristic properties of supercohomology phases - namely, symmetry fractionalization on fermion parity flux loops - predicted by continuum formulations. By composing the corresponding FDQCs, we also recover the stacking relations of supercohomology phases. Furthermore, we derive topologically ordered gapped boundaries for the supercohomology models by extending the protecting symmetries, analogous to the construction of topologically ordered boundaries for bosonic SPT phases. Our approach relies heavily on dualities that relate certain bosonic 2-group SPT phases with supercohomology SPT phases. We develop physical motivation for the dualities in terms of explicit lattice prescriptions for gauging a 1-form symmetry and for condensing emergent fermions. We also comment on generalizations to supercohomology phases in higher dimensions and to fermionic SPT phases outside of the supercohomology framework.Comment: 28+25 pages, 31 figure

Flexible and waterproof micro-sensors to uncover zebrafish circadian rhythms: The next generation of cardiac monitoring for drug screening

Flexible electronics are the next generation of sensors for mobile health and implantation. Zebrafish (Danio rerio) is an emergent strategy for pre-clinical drug development and toxicity testing. To address the confounding effects from sedation of fish and removal from the aquatic habitat for micro-electrocardiogram (µECG) measurements, we developed waterproof and wearable sensors to uncover the circadian variation in heart rate (HR) and heart rate variability (HRV) ( Massin et al., 2000). The parylene-C based ECG sensor consisted of an ultra-soft silicone integrated jacket designed to wrap around the fish during swimming. The Young’s modulus of this silicone jacket matched with the fish surface, and an extended parylene cable connected the underwater chest electrodes with the out-of water electronics. In addition, embedded micro-glass spheres in the silicone effectively reduced the effective density of the jacket to ~1 g cm^(−3). These innovations enabled physiological ECG telemetry in the fish’s natural habitat without the need for sedation. Furthermore, a set of non-linear signal processing techniques filtered out the breathing and electromagnetic artifacts from the recorded signals. We observed a reduction in mean HR and an increase in HRV over 24 h at 10 dpa, accompanied by QT prolongation as well as diurnal variations, followed by normalization in mean HR and QT intervals at 26 days post ventricular amputation (dpa). We revealed Amiodarone-mediated QTc prolongation, HR reduction and HRV increase otherwise masked by sedation. The novel features of the flexible silicon jacket for µECG telemetry unraveled the biological clock and normalization of QT intervals at 26 dpa, providing the first evidence of new physiological phenomena during cardiac injury and repair as well as cardiac drug-mediated aberrant rhythms. Thus, the light weight and waterproof design holds promise to advance the next generation of mobile health and drug discovery

Pauli topological subsystem codes from Abelian anyon theories

We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the $\mathbb{Z}_4^{(1)}$ anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes. The construction proceeds by "gauging out" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higher-form symmetries.Comment: 67 + 35 pages, single column forma

Causal Mediation Analysis with Multiple Time-Varying Mediators

In longitudinal studies with time-varying exposures and mediators, the mediational g-formula is an important method for the assessment of direct and indirect effects. However, current methodologies based on the mediational g-formula can deal with only one mediator. This limitation makes these methodologies inapplicable to many scenarios. Hence, we develop a novel methodology by extending the mediational g-formula to cover cases with multiple time-varying mediators. We formulate two variants of our approach that are each suited to a distinct set of assumptions and effect definitions and present nonparametric identification results of each variant. We further show how complex causal mechanisms (whose complexity derives from the presence of multiple time-varying mediators) can be untangled. A parametric method along with a user-friendly algorithm was implemented in R software. We illustrate our method by investigating the complex causal mechanism underlying the progression of chronic obstructive pulmonary disease. We found that the effects of lung function impairment mediated by dyspnea symptoms and mediated by physical activity accounted for 13.7% and 10.8% of the total effect, respectively. Our analyses thus illustrate the power of this approach, providing evidence for the mediating role of dyspnea and physical activity on the causal pathway from lung function impairment to health status

Formalizing Chemical Physics using the Lean Theorem Prover

Chemical theory can be made more rigorous using the Lean theorem prover, an interactive theorem prover for complex mathematics. We formalize the Langmuir and BET theories of adsorption, making each scientific premise clear and every step of the derivations explicit. Lean's math library, mathlib, provides formally verified theorems for infinite geometries series, which are central to BET theory. While writing these proofs, Lean prompts us to include mathematical constraints that were not originally reported. We also illustrate how Lean flexibly enables the reuse of proofs that build on more complex theories through the use of functions, definitions, and structures. Finally, we construct scientific frameworks for interoperable proofs, by creating structures for classical thermodynamics and kinematics, using them to formalize gas law relationships like Boyle's Law and equations of motion underlying Newtonian mechanics, respectively. This approach can be extended to other fields, enabling the formalization of rich and complex theories in science and engineering

Gene Alterations of Ovarian Cancer Cells Expressing Estrogen Receptors by Estrogen and Bisphenol A Using Microarray Analysis

Since endocrine disrupting chemicals (EDCs) may interfere with the endocrine system(s) of our body and have an estrogenicity, we evaluated the effect(s) of bisphenol A (BPA) on the transcriptional levels of altered genes in estrogen receptor (ER)-positive BG-1 ovarian cancer cells by microarray and real-time polymerase-chain reaction. In this study, treatment with 17β-estradiol (E2) or BPA increased mRNA levels of E2-responsive genes related to apoptosis, cancer and cell cycle, signal transduction and nucleic acid binding etc. In parallel with their microarray data, the mRNA levels of some altered genes including RAB31_MEMBER RAS ONCOGENE FAMILY (U59877), CYCLIN D1 (X59798), CYCLIN-DEPENDENT KINASE 4 (U37022), IGF-BINDING PROTEIN 4 (U20982), and ANTI-MULLERIAN HORMONE (NM_000479) were significantly induced by E2 or BPA in this cell model. These results indicate that BPA in parallel with E2 induced the transcriptional levels of E2-responsive genes in an estrogen receptor (ER)-positive BG-1 cells. In conclusion, these microarray and real-time polymerase-chain reaction results indicate that BPA, a potential weak estrogen, may have estrogenic effect by regulating E2-responsive genes in ER-positive BG-1 cells and BG-1 cells would be the best in vitro model to detect these estrogenic EDCs