Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page

Automatic Design of Synthetic Gene Circuits through Mixed Integer Non-linear Programming

Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits

Demographic Diversity and Sustainable Fisheries

Fish species are diverse. For example, some exhibit early maturation while others delay maturation, some adopt semelparous reproductive strategies while others are iteroparous, and some are long-lived and others short-lived. The diversity is likely to have profound effects on fish population dynamics, which in turn has implications for fisheries management. In this study, a simple density-dependent stage-structured population model was used to investigate the effect of life history traits on sustainable yield, population resilience, and the coefficient of variation (CV) of the adult abundance. The study showed that semelparous fish can produce very high sustainable yields, near or above 50% of the carrying capacity, whereas long-lived iteroparous fish can produce very low sustainable yields, which are often much less than 10% of the carrying capacity. The difference is not because of different levels of sustainable fishing mortality rate, but because of difference in the sensitivity of the equilibrium abundance to fishing mortality. On the other hand, the resilience of fish stocks increases from delayed maturation to early maturation strategies but remains almost unchanged from semelparous to long-lived iteroparous. The CV of the adult abundance increases with increased fishing mortality, not because more individuals are recruited into the adult stage (as previous speculated), but because the mean abundance is more sensitive to fishing mortality than its standard deviation. The magnitudes of these effects vary depending on the life history strategies of the fish species involved. It is evident that any past high yield of long-lived iteroparous fish is a transient yield level, and future commercial fisheries should focus more on fish that are short-lived (including semelparous species) with high compensatory capacity

Spatial and Seasonal Distribution of American Whaling and Whales in the Age of Sail

American whalemen sailed out of ports on the east coast of the United States and in California from the 18th to early 20th centuries, searching for whales throughout the world’s oceans. From an initial focus on sperm whales (Physeter macrocephalus) and right whales (Eubalaena spp.), the array of targeted whales expanded to include bowhead whales (Balaena mysticetus), humpback whales (Megaptera novaeangliae), and gray whales (Eschrichtius robustus). Extensive records of American whaling in the form of daily entries in whaling voyage logbooks contain a great deal of information about where and when the whalemen found whales. We plotted daily locations where the several species of whales were observed, both those caught and those sighted but not caught, on world maps to illustrate the spatial and temporal distribution of both American whaling activity and the whales. The patterns shown on the maps provide the basis for various inferences concerning the historical distribution of the target whales prior to and during this episode of global whaling

Amphibole and apatite insights into the evolution and mass balance of Cl and S in magmas associated with porphyry copper deposits

Chlorine and sulfur are of paramount importance for supporting the transport and deposition of ore metals at magmatic–hydrothermal systems such as the Coroccohuayco Fe–Cu–Au porphyry–skarn deposit, Peru. Here, we used recent partitioning models to determine the Cl and S concentration of the melts from the Coroccohuayco magmatic suite using apatite and amphibole chemical analyses. The pre-mineralization gabbrodiorite complex hosts S-poor apatite, while the syn- and post-ore dacitic porphyries host S-rich apatite. Our apatite data on the Coroccohuayco magmatic suite are consistent with an increasing oxygen fugacity (from the gabbrodiorite complex to the porphyries) causing the dominant sulfur species to shift from S2− to S6+ at upper crustal pressure where the magmas were emplaced. We suggest that this change in sulfur speciation could have favored S degassing, rather than its sequestration in magmatic sulfides. Using available partitioning models for apatite from the porphyries, pre-degassing S melt concentration was 20–200 ppm. Estimates of absolute magmatic Cl concentrations using amphibole and apatite gave highly contrasting results. Cl melt concentrations obtained from apatite (0.60 wt% for the gabbrodiorite complex; 0.2–0.3 wt% for the porphyries) seems much more reasonable than those obtained from amphibole which are very low (0.37 wt% for the gabbrodiorite complex; 0.10 wt% for the porphyries). In turn, relative variations of the Cl melt concentrations obtained from amphibole during magma cooling are compatible with previous petrological constraints on the Coroccohuayco magmatic suite. This confirms that the gabbrodioritic magma was initially fluid undersaturated upon emplacement, and that magmatic fluid exsolution of the gabbrodiorite and the pluton rooting the porphyry stocks and dikes were emplaced and degassed at 100–200 MPa. Finally, mass balance constraints on S, Cu and Cl were used to estimate the minimum volume of magma required to form the Coroccohuayco deposit. These three estimates are remarkably consistent among each other (ca. 100 km3) and suggest that the Cl melt concentration is at least as critical as that of Cu and S to form an economic mineralization

Occupation of racial grief, loss as a resource : learning from ‘The Combahee River Collective Black Feminist Statement'

The methodology of ‘occupation’ through rereading The Combahee River Collective Black Feminist Statement (The Combahee River Collective, in: James, Sharpley-Whiting (eds) The Black Feminist Reader. Blackwell Publishers Ltd., Oxford, pp 261–270, 1977) demonstrates the necessity of temporal linkages to historical Black feminist texts and the wisdom of Black feminist situated knowers. This paper argues that racism produces grief and loss and as long as there is racism, we all remain in racial grief and loss. However, in stark contrast to the configuration of racial grief and loss as something to get over, perhaps grief and loss can be thought about differently, for example, in terms of racial grief and loss as a resource. This paper questions Western Eurocentric paternalistic responses to Black women’s ‘talk about their feelings of craziness… [under] patriarchal rule’ (The Combahee River Collective 1977: 262) and suggests alternative ways of thinking about the psychological impact of grief and loss in the context of racism. In this paper, a Black feminist occupation of racial grief and loss includes the act of residing within, and the act of working with the constituent elements of racial grief and loss. The proposal is that an occupation of racial grief and loss is a paradoxical catalyst for building a twenty-first century global intersectional Black feminist movement