Control barrier functions (CBFs) have been widely applied to safety-critical robotic applications. However, the construction of control barrier functions for robotic systems remains a challenging task. Recently, collision detection using differentiable optimization has provided a way to compute the minimum uniform scaling factor that results in an intersection between two convex shapes and to also compute the Jacobian of the scaling factor. In this letter, we propose a framework that uses this scaling factor, with an offset, to systematically define a CBF for obstacle avoidance tasks. We provide theoretical analyses of the continuity and continuous differentiability of the proposed CBF. We empirically evaluate the proposed CBF's behavior and show that the resulting optimal control problem is computationally efficient, which makes it applicable for real-time robotic control. We validate our approach, first using a 2D mobile robot example, then on the Franka-Emika Research 3 (FR3) robot manipulator both in simulation and experiment.

The Deccan Volcanic Province (DVP), covering presently an area of 0.5 million km², and estimated to be 2–3 times larger during the Upper Cretaceous-Paleocene, is one of the largest continental flood basalt provinces of the world. Its formation has been linked to the foundering of the Gondwanaland and Greater India’s northward drift, passing over the Reunion plume and eruption of over a million km³ of lava that apparently led to a mass extinction of global proportions. The DVP has thus been a major domain of scientific interest and study the world over. It had received attention since the 1830s, first from the army and civil service men of the British Raj and subsequently from the officers of the Geological Survey of India (GSI) founded in 1851, and academicians from a number of Indian Universities and research Institutions, often in collaboration with geologists from countries such as the UK, USA, Russia, France, Japan, Italy and others. Thus, studies of the DVP conducted for over 170 years, and especially in the last five decades, have provided a very large database that has led to a better understanding of the genesis and evolution of the this province and similar flood basalt provinces of the world. The DVP is thickest in the Western Ghats, forming many individual 400 m to 1650 m thick sections over some 700 km. The structural evolution of the lava sequence envisages a pre-uplift, thick (c. 2–3 km), lensoid pile of dense basalt that gradually sank into the crust by the end of the eruptive phase, followed by an uplift of the western margin of the Deccan due to both denudational-isostasy reasons and the associated geomorphological and structural evolution of the lava pile from Tertiary uplift and coastal flexure formation (the Panvel structure). Such an evolution has led to stresses that get accommodated along fractures in the pre-Deccan basement at varying depths and apparently provide the loci for seismicity observed over the province. The DVP is predominantly composed of quartz- and hypersthene-normative tholeiitic basalts in the plateau regions (Western Ghats and adjoining central and eastern parts, Malwa and Mandla). However, along the ENE-WSW-trending Narmada-Tapi rift zones, the N-S to NNW-SSE-trending Western coastal tract, the Cambay rift zone, and the Saurashtra and Kutch regions, the DVP shows considerable diversity in terms of structures, dyke swarms and dyke clusters, and intrusive and extrusive centres with diverse rock types. These include: primary picrite basalts and their differentiates (e.g., Botad, Dhandhuka, Wadhwan Jn., Pavagadh), granophyre-rhyolite intrusive ring-complexes and mixed basalt-rhyolite associations (e.g., Alech, Barda, Osham, Chogat-Chamardi, Mumbai Island, and others), carbonatite-nephelinite associations (Amba Dongar-Kawant), gabbro-anorthosite-nepheline syenite-syenite ring/layered complexes(e.g., Mt. Girnar, Mundwara, Phenai Mata), mantle-derived spinel peridotite-hosting melanephelinites and basanites (e.g. Dhrubya, Vethon and others in Kutch), besides scores of alkaline and lamprophyre dykes. Some of these complexes are associated with high gravity anomalies indicating dense plutonic bodies at depths. Flow morphological studies of the DVP have led to the recognition of two main types of flows, namely ‘a’a (typically forming simple, sheet flows) and pâhoehoe (typically forming compound, pahoehoe lobate flows) with transitions between them that result in mixed types. The ‘a’a types are largely single units found in the peripheral parts where thicknesses of the flow sequence range from a few meters to a few tens of meters. The compound pâhoehoe flows contain many units or lobes and are largely found in the thicker sections of Western Ghats, and also in the central parts of the province. The flow sequences of the Western Ghats (c. 400 m to 1650 m thick and spread over an area of400 km × 100 km along the N-S tract from north of Nasik to Belgaum) have been mapped and correlated using flow morphology, petrology and selected trace elements (Sr, Ba, Zr, Y and Ti) and Sr- isotopes. Such a combination of geochemical characters, constrained further by altitude and magnetic polarity (chrons 30N-29R-29N) have led to the delineation of the flow sequences from north to south into a Deccan Basalt Group, comprising three Subgroups from the base to the top, namely the Kalsubai, Lonavala and Wai Subgroups, with twelve (12) formations in total, each formation containing many flows. Giant plagioclase basalts (GPBs) and bole beds of diverse origin (intertrappean sediments, weathered basalt or tuffs with baking effects) have been found in many flow sequences of the DVP, especially in the Western Ghats and contiguous plateau regions, and these interflow units help in subregional-scale mapping and also provide insights into magma chamber processes and eruptive breaks in the volcanic cycles. Field and geochemical studies of some twenty-three (23) flow sequences (10 from Western Ghats, five from central India and eight from eastern India) by several groups have enabled correlation of some formations of the Western Ghats such as the Ambenali (crustally uncontaminated) and Poladpur (contaminated) over long distances (c. 400–700 km) to Toranmal, Mhow, Chikaldara, Jabalpur and other sections. However, these formations occur at different stratigraphie elevations at these places and also differ in some isotopic characters (e.g. ²⁰⁶Pb/²⁰⁴Pb). Such features have cast doubts on long distance travel of flows from a single source and led to suggestions of multiple source areas (vents and dykes) as also inferred from the two zones of compositional diversity mentioned above. Based on detailed field, petrological and geochemical characters including isotopic data and Ar-Ar ages, dyke swarms and clusters in the Narmada-Tapi and western coastal tracts have been shown to belong to two groups: (1) The randomly oriented group between Pune and Nasik as possible feeders to the lava flow sequences of the Western Ghats and (2) Some of the dykes from the east-west-oriented Narmada-Tapi swarm, attributed to active N-S extension during the flood basalt episode, and showing chemical affinities to the lower and middle formations (Jawhar, Igatpuri, Neral, Thakurwadi, Bhimashankar, Khandala). A wide variety of petrographic types of basalts have been observed in the DVP attesting to the diverse crystallisation and differentiation of the different magma types during transport and in magma chambers. Based on petrographic and mineralogical data from a number of thick sections, it has been inferred that minerals such as olivine (Fo₉₀–Fo₂₀), clinopyroxenes (diopsidic augite, augite, subcalcic augite and pigeonite), plagioclase (An₈₄–An₃₀) and opaque oxides including spinels show considerable variations depending upon the tholeiitic or alkaline character of the host magma and its degree of evolution. Secondary minerals, especially zeolites such as heulandite and stilbite, are found in all the ten formations of the Western Ghats whereas merlionite and analcite are only found in the Khandala Formation. Other ten species are of variable abundance are found in the ten formations of the Western Ghats and other areas. Zeolite zonation in DVP suggested earlier has not been substantiated by recent studies, instead multigeneration of secondary minerals in cavities is attributed to late hydrothermal activity from Paleocene to early Miocene.

Malware can range from simple adware to stealthy kernel control-flow modifying rootkits. Although anti-virus software is popular, an ongoing cat-and-mouse cycle of anti-virus development and malware that thwarts the anti-virus has ensued. More recently, trusted hardware-based malware detection techniques are being developed on the premise that it is easier to bypass software-based defenses than hardware-based counterparts. One such approach is the use of hardware performance counters (HPCs) to detect malware for Linux and Android platforms. This paper, for the first time, presents an analytical framework to investigate the security provided by HPC-based malware detection techniques. The HPC readings are periodically monitored over the duration of the program execution for comparison with a golden HPC reading. We develop a mathematical framework to investigate the probability of malware detection, when HPCs are monitored at a pre-determined sampling interval. In other words, given a program, a set of HPCs, and a sampling rate, the framework can be employed to analyze the probability of malware detection.

Malicious modifications to printed circuit boards (PCBs) are known as hardware Trojans. These may arise when malafide third parties alter PCBs premanufacturing or postmanufacturing and are a concern in safety-critical applications, such as industrial control systems. In this research, we examine how data-driven detection can be utilized to detect such Trojans at run-time. We develop a flexible and reconfigurable PCB test bed derived from the popular open-source programmable logic controller (PLC) platform “OpenPLC.” We then develop a Trojan detection framework, which utilizes and analyzes multimodal side channels (e.g., timing, magnetic signals, power, and hardware performance counters). We consider defender-configurable input/output (I/O) loopback test, comparison with design-document baselines, and magnetometer-aided monitoring of system behavior under defender-chosen excitations. Our approach can extend to golden-free environments. Golden (known-good) versions of the PCBs are assumed not available, but design information, datasheets, and component-level data are available. We demonstrate the efficacy of our approach on a range of Trojans instantiated in the test bed.

Based on the field relations, associated rock types and age, the carbonatite-alkaline rock complexes of India, that are spatially related to deep main faults, rifts and shear zones, have been classified in to two major groups, namely: 1. Middle — late Cretaceous, subvolcanic -volcanic complexes (Amba Dongar, Siriwasan, Swangkre, Mer-Mundwara, Sarnu-Dandali-Kamthai) and 2. Paleo-Neoproterozoic plutonic complexes (Newania, Sevathur, Samalpatti, Hogenakal, Kollegal, Pakkanadu, Udaiyapatti, Munnar, and Khambamettu). The middle Cretaceous Sung Valley and Samchampi complexes also belong to this plutonic group. Three minor associations, belonging to these two age groups include, the Neoproterzoic, late stage veins of carbonatites in peralkaline syenite complexes (e.g., Kunavaram, Elchuru), the diamond-bearing carbonatite and kimberlite at Khaderpet and the lamprophyre-lamproite association (e.g., Pachcham Is. Upper Cretaceous, Deccan Volcanic Province, and the Proterozoic Chitrangi Group). Petrological associations include carbonatite-nephelinite-phonolite (e.g. Amba Dongar, Sarnu-Dandali-Kamthai), dunite-peridotite-pyroxenite-ijolitemelilitite (e.g. Sung Valley), miaskitic syenite-pyroxenite ± dunite (e.g. Sevathur, Samalpatti, Pakkanadu), carbonatite alone with fenites (e.g. Newania), besides those minor associations mentioned above. Sovites (calico-carbonatites) occur as the most dominant type in some ten (10) complexes. Beforsite (magnesio-carbonatite) is the dominant type at Newania and ankeritic-sideritic types are mainly found at Amba Dongar, Siriwasan and Newania. The rare benstonite-bearing carbonatites are found at Jokkipatti and Udaiyapatti in Tamil Nadu. Mineralogically and chemically the carbonatites show considerable diversity. Fenitised zones and types of fenites (Na, K and mixed) vary widely since the carbonatites are emplaced in a variety of hostrocks ranging from granitic, mafic, ultramafic, charnockitic types besides basalts and sandstones. Stable (δ¹³C and δ¹⁸O) and radiogenic (Sr, Nd and Pb) isotopes clearly indicate their mantle origin and also the diverse types of sources (both depleted HIMU and enriched EM 1 and 2). Petrogenetic considerations reveal three types of carbonatites, namely direct partial melts from metasomatised mantle (e.g. Newania), liquid immiscibility from carbonatite-nephelinite association (e.g. Amba Dongar) and through fractionation of ultra-alkaline ultramafic and mafic association (e.g. Sung Valley). Carbonatites of India that host significant resources include Amba Dongar (Fluorite, REE, Nb, P, Ba, Sr), Kamthai (REE), Sevathur (Nb, P, vermiculite), Beldih (P, Fe), Sung Valley (P, Nb, REE, Fe) and Samchampi (P, Nb, Fe, REE).