Detailed balance and projectability conditions are two main assumptions when Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz (HL) theory. While the latter represents an important ingredient, the former often believed needs to be abandoned, in order to obtain an ultraviolet stable scalar field, among other things. In this paper, because of several attractive features of this condition, we revisit it, and show that the scalar field can be stabilized, if the detailed balance condition is allowed to be softly broken. Although this is done explicitly in the non-relativistic general covariant setup of Horava-Melby-Thompson with an arbitrary coupling constant λ, generalized lately by da Silva, it is also true in other versions of the HL theory. With the detailed balance condition softly breaking, the number of independent coupling constants can be still significantly reduced. It is remarkable to note that, unlike other setups, in this da Silva generalization, there exists a master equation for the linear perturbations of the scalar field in the flat Friedmann-Robertson-Walker background.

We present a Lorentz gauge theory of gravity in which the metric is not dynamical. Spherically symmetric weak field solutions are studied. We show that this solution contains the Schwarzschild spacetime at least to the first order of perturbation. Next, we present a special case of the theory where the Schwarzschild metric is an exact solution. It is also shown that the de Sitter space is an exact vacuum solution of this special case and as a result the theory is able to explain the expansion of the universe with no need for dark energy. Within this special case, quantization of the theory is also studied, the basic Feynman diagrams are derived and the renormalizability of the theory is studied using the power-counting method. We show that under a certain condition the theory is power-counting renormalizable.

Brain organoids recapitulate a number of brain properties, including neuronal diversity. However, do they recapitulate brain structure? Using a hydrodynamic description for cell nuclei as particles interacting initially via an effective, attractive force as mediated by the respective, surrounding cytoskeletons, we quantify structure development in brain organoids to determine what physical mechanism regulates the number of cortex-core structures. Regions of cell nuclei overdensity in the linear regime drive the initial seeding for cortex-core structures, which ultimately develop in the non-linear regime, as inferred by the emergent form of an effective interaction between cell nuclei and with the extracellular environment. Individual cortex-core structures then provide a basis upon which we build an extended version of the buckling without bending morphogenesis (BWBM) model, with its proliferating cortex and constraining core, to predict foliations/folds of the cortex in the presence of a nonlinearity due to cortical cells actively regulating strain. In doing so, we obtain asymmetric foliations/folds with respect to the trough (sulci) and the crest (gyri). In addition to laying new groundwork for the design of more familiar and less familiar brain structures, the hydrodynamic description for cell nuclei during the initial stages of brain organoid development provides an intriguing quantitative connection with large-scale structure formation in the universe.

Modeling living systems at the collective scale can be very challenging because the individual constituents can themselves be complex and the respective interactions between the constituents may not be fully understood. With the advent of high throughput experiments and in the age of big data, data-driven methods are on the rise to overcome these challenges. Although machine-learning approaches can help quantify correlations between the various players, they do not directly shed light on the underlying physical principles of such systems. Here, we present a data-driven method for obtaining the phase-space density of active matter systems such that the solution to the stochastic dynamic equation for active matter readily emerges, from which time and space dependence of physical order parameters can be readily extracted. If the system is near a steady state, we illuminate how to construct a field theory to subsequently make physical predictions about the system. The method is first developed analytically and subsequently calibrated using simulated data. The method is then applied to an experimental system of particles actively driven by a {\it Serratia marcescens} bacterial swarm and in the presence of localized UV light. The analysis demonstrates that the particles are in the steady-state before and sometime after the UV light and obey a Gaussian field theory with a spatially-varying ``mass'' in those regimes. This novel yet simple finding is surprising given the complex dynamics of the bacterial swarm. In response to the UV light, we demonstrate that there is a net flow of the particles away from the UV light and that the entropy of the particles increases away from the light. We conclude with a discussion of additional potential applications of our data-driven method such as when the internal structure of the individual constituents dynamically changes to result in a modified stochastic dynamic equation governing the system.