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Experiencing intense flashbacks, nightmares, irritability, anger, and fear? In the face of a traumatic event like the Covid-19 pandemic, it’s common to feel this way.

We review some recent results on the phenomenon of surface superconductivity in the framework of Ginzburg-Landau theory for extreme type-II materials. In particular, we focus on the response of the superconductor to a strong longitudinal magnetic field in the regime where superconductivity survives only along the boundary of the wire. We derive the energy and density asymptotics for samples with smooth cross section, up to curvature-dependent terms. Furthermore, we discuss the corrections in presence of corners at the boundary of the sample.

We prove the effectiveness of the canonical bundle of several Hurwitz spaces of degree k covers of the projective line from curves of genus 13<g<20.

We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic, assuming perfect knowledge of the ambient elevation data and human walking velocity as a function of local slope of the terrain. Our model includes a stochastic component which can account for uncertainty in the problem, and thus includes a Hamilton-Jacobi-Bellman equation with viscosity. We discuss the model in the presence and absence of stochastic effects, and suggest numerical methods for simulating the model. We discuss two different notions of an optimal path when there is uncertainty in the problem. Finally, we compare the optimal paths suggested by the model at different levels of uncertainty, and observe that as the size of the uncertainty tends to zero (and thus the viscosity in the equation tends to zero), the optimal path tends toward the deterministic optimal path.

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $ngeq 3$ and there is no odd cycle without chord and length at least 5.

Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore sizes are less than 50 nm. At this scale, the fluid properties are affected by nanoconfinement effects due to the increased fluid-solid interactions. For instance, gas adsorption to the pore walls could account for up to 85% of the total hydrocarbon volume in a tight reservoir. Although there are analytical solutions that describe this phenomenon for simple geometries, they are not suitable for describing realistic pores, where surface roughness and geometric anisotropy play important roles. To describe these, molecular dynamics (MD) simulations are used since they consider fluid-solid and fluid-fluid interactions at the molecular level. However, MD simulations are computationally expensive, and are not able to simulate scales larger than a few connected nanopores. We present a method for building and training physics-based deep learning surrogate models to carry out fast and accurate predictions of molecular configurations of gas inside nanopores. Since training deep learning models requires extensive databases that are computationally expensive to create, we employ active learning (AL). AL reduces the overhead of creating comprehensive sets of high-fidelity data by determining where the model uncertainty is greatest, and running simulations on the fly to minimize it. The proposed workflow enables nanoconfinement effects to be rigorously considered at the mesoscale where complex connected sets of nanopores control key applications such as hydrocarbon recovery and CO2 sequestration.

When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. This paper aims to investigate the effect of geometric approximation error by using a high-order mesh with negligible geometric approximation error, even for high order polynomial of order p. To achieve this goal, the high-order mesh generator from CAD geometry called NekMesh is adapted for surface mesh generation in comparison to traditional meshes with non-negligible geometric approximation error. Two types of numerical tests are considered. Firstly, the accuracy of differential operators is compared for various p on a curved element of the sphere. Secondly, by applying the method of moving frames, four different time-dependent PDEs on the sphere are numerically solved to investigate the impact of geometric approximation error on the accuracy and conservation properties of high-order numerical schemes for PDEs on the sphere.

We study the problem of pricing under a Multinomial Logit model where we incorporate network effects over the consumer's decisions. We analyse both cases, when sellers compete or collaborate. In particular, we pay special attention to the overall expected revenue and how the behaviour of the no purchase option is affected under variations of a network effect parameter. Where for example we prove that the market share for the no purchase option, is decreasing in terms of the value of the network effect, meaning that stronger communication among costumers increases the expected amount of sales. We also analyse how the customer's utility is altered when network effects are incorporated into the market, comparing the cases where both competitive and monopolistic prices are displayed. We use tools from stochastic approximation algorithms to prove that the probability of purchasing the available products converges to a unique stationary distribution. We model that the sellers can use this stationary distribution to establish their strategies. Finding that under those settings, a pure Nash Equilibrium represents the pricing strategies in the case of competition, and an optimal (that maximises the total revenue) fixed price characterise the case of collaboration.

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A catastrophic loss in biodiversity, reckless destruction of wildland and warming temperatures have allowed disease to explode. Ignoring the connection between climate change and pandemics would be “dangerous delusion,” one scientist said. The scientists who study how diseases emerge in a changing environment knew this moment was coming.…

A method of treating hepatitis virus infection is disclosed. The method comprising administering to a human subject in need of such treatment an effective hepatitis virus-combatting amount of an alkyl lipid or alkyl lipid derivative.

A method of treating hepatitis virus infection is disclosed. The method comprising administering to a human subject in need of such treatment an effective hepatitis virus-combatting amount of an alkyl lipid or alkyl lipid derivative.

Shape memory and pseudoelastic martensitic behavior is enabled by a structure in which there is provided a crystalline ceramic material that is capable of undergoing a reversible martensitic transformation and forming martensitic domains, during such martensitic transformation, that have an elongated domain length. The ceramic material is configured as a ceramic material structure including a structural feature that is smaller than the elongated domain length of the ceramic material.

A method includes determining a read threshold voltage corresponding to a group of storage elements in a non-volatile memory that includes a three-dimensional (3D) memory of a data storage device. The method also includes determining an error metric corresponding to data read from the group of storage elements using the read threshold voltage. The method includes comparing the read threshold voltage and the error metric to one or more criteria corresponding to a corrupting event.

The invention provides a method and apparatus for creating plasma particles and applying the plasma particles to a liquid. Liquid feedstock (e.g., water and/or hydrocarbons mixed with biomass) is pumped through a pipeline; the single-phase stream is then transformed into a biphasic liquid-and-gas stream inside a chamber. The transformation is achieved by transitioning the stream from a high pressure zone to a lower-pressure zone. The pressure drop may occur when the stream further passes through a device for atomizing liquid. Inside the chamber, an electric field is generated with an intensity level that exceeds the threshold of breakdown voltage of the biphasic medium leading to a generation of a plasma state. Furthermore, the invention provides an energy-efficient highly adaptable and versatile method and apparatus for sanitizing water using plasma particles to inactivate biological agents contaminating water.

The invention relates to polymers that can be obtained by polymerizing the monomers (A), (B), and (D), and optionally (C), where (A) is a monomer of formula (I), wherein A stands for C2 to C4 alkylene, B stands for a C2 to C4 alkylene different from A, R stands for hydrogen or methyl, m stands for a number from 1 to 500, n stands for a number from 1 to 500, (B) is an ethylenically unsaturated monomer that contains at least one carboxylic acid function, (C) is optionally a further ethylenically unsaturated monomer different from (A) and (B), (D) is a monomer of formula (II), wherein D stands for C2 to C4 alkylene, E stands for a C2 to C4 alkylene group different from D, F stands for a C2 to C4 alkylene group different from E, R stands for hydrogen or methyl, o stands for a number from 1 to 500, p stands for a number from 1 to 500, q stands for a number from 1 to 500, and wherein the weight fraction of the monomers is 35 to 99% for the macromonomer (A), 0.5 to 45% for the monomer (B), 0 to 20% for the monomer (C), and 1 to 20% for the monomer (D), and to the use of said polymers as defoamers for inorganic solid suspensions.

A method is provided to manage program code that runs in a computer system comprising: producing a management information structure that identifies a managed system within the computer system; producing a master object definition information structure that provides a mapping between master objects and corresponding managed code objects that run in the computer system; and requesting extraction of information from the managed system identified by the master information structure that relates to managed code objects that the object definition information structure maps to master objects.

Aspects of the invention relate to techniques of defect injection for transistor-level fault simulation. A circuit element in a circuit netlist of a circuit is first selected for defect injection. Next, a defect is determined based on whether the selected circuit element is a design-intent circuit element or a parasitic circuit element. After the defect is determined, the defect is injected into the circuit netlist and then the circuit is simulated.

A pharmaceutical composition comprising lectins is anti-tumorigenic and anti-viral, bacterial or protozoan. The composition, termed BiOmune is also useful for imaging, diagnosis and therapy of cancer.

A device and method for accurately characterizing tissue impedance employs multiple electrodes at a plurality of separation distances to cancel the effects of front end loading leakage currents and electrode polarization to improve the accuracy of sensitive impedance measurements used to identify cancerous tissues. These measurements may be automated over a range of frequencies.

In a method for simulating temperature and electrical characteristics within an circuit, a temperature of at least one volume within the circuit as a function of a resistance within the at least one volume is repeatedly calculated and the resistance as a function of the temperature is repeatedly calculated until the temperature is within a predetermined tolerance of a previous temperature result and until the resistance is within a predetermined tolerance of a previous resistance result. Once the temperature is within a predetermined tolerance of the previous temperature result and the resistance is within a predetermined tolerance of the previous resistance, then an output indicative of the temperature is generated.

The embodiments relate to modeling resistance in a multi-fin multi-gate field effect transistor (MUGFET). In these embodiments, a design for a multi-fin MUGFET comprises a gate structure with a horizontal portion traversing multiple semiconductor fins and comprising a plurality of first resistive elements connected in series, with vertical portions adjacent to opposing sides of the semiconductor fins and comprising second resistive elements connected in parallel by the horizontal portion, and with contact(s) comprising third resistive element(s). The total gate resistance is determined based on resistance contributions from the first resistive elements, the second resistive elements and the third resistive element(s), particularly, where each resistive contribution is based on a resistance value of the resistive element, a first fraction of current from the semiconductor fins entering the resistive element and a second fraction of the current from the semiconductor fins exiting the resistive element.

Disclosed are polysulfone-based materials that can be used as active and/or passive components in various electronic, optical, and optoelectronic devices, particularly, metal-oxide-semiconductor field-effect transistors. For example, various metal-oxide-semiconductor field-effect transistors can include a dielectric layer and/or a passivation layer prepared from such polysulfone-based materials and exhibit good device performance.

One or more temporal stimulation parameters of vagus nerve stimulation (VNS) are selected to substantially modulate one or more target physiological functions without substantially modulating one or more non-target physiological functions. In one embodiment, a stimulation duty cycle is selected such that VNS is delivered to the cervical vagus nerve trunk to modulate a cardiovascular function without causing laryngeal muscle contractions.

A method is disclosed for preparing a soft tissue site, and augmenting the soft tissue site, such as the breast(s), scar, depression, or other defect, of a subject through use of devices that exert a distractive force on the breast(s) and grafting of autologous fat tissue such as domes with sealing rims for surrounding each of the soft tissue site and a regulated pump. The method for preparing the soft tissue site, and enhancing fat graft results, entails application of the distracting force to the targeted soft tissue site at least intermittently for some period of time and preferably several weeks prior to the graft procedure. A related aspect of the invention includes following the preparation steps by transfer of fat from other areas of the subject to the subject's soft tissue site, and then reapplication of the distractive force to the soft tissue site that received the autologous fat graft. Alternatively, fat from genetically related sources may be used, and the fat may be further processed prior to injection. Substantial soft tissue augmentation, high rates of graft survival and negligible graft necrosis (data demonstrating 80% survival and only 20% necrosis is presented) or calcification result from the practice of these methods.

This invention relates to novel compounds which are inhibitors of the Rearranged during Transfection (RET) kinase, to pharmaceutical compositions containing them, to processes for their preparation, and to their use in therapy, alone or in combination, for the normalization of gastrointestinal sensitivity, motility and/or secretion and/or abdominal disorders or diseases and/or treatment related to diseases related to RET dysfunction or where modulation of RET activity may have therapeutic benefit including but not limited to all classifications of irritable bowel syndrome (IBS) including diarrhea-predominant, constipation-predominant or alternating stool pattern, functional bloating, functional constipation, functional diarrhea, unspecified functional bowel disorder, functional abdominal pain syndrome, chronic idiopathic constipation, functional esophageal disorders, functional gastroduodenal disorders, functional anorectal pain, inflammatory bowel disease, proliferative diseases such as non-small cell lung cancer, hepatocellular carcinoma, colorectal cancer, medullary thyroid cancer, follicular thyroid cancer, anaplastic thyroid cancer, papillary thyroid cancer, brain tumors, peritoneal cavity cancer, solid tumors, other lung cancer, head and neck cancer, gliomas, neuroblastomas, Von Hippel-Lindau Syndrome and kidney tumors, breast cancer, fallopian tube cancer, ovarian cancer, transitional cell cancer, prostate cancer, cancer of the esophagus and gastroesophageal junction, biliary cancer, adenocarcinoma, and any malignancy with increased RET kinase activity.

A combination trimming/flame treatment end effector adapted for mounting to the end of a robotic arm. A trimming blade extends from a main body portion of the end effector for performing a trimming operation. The trimming blade may be mounted in an exchangeable cartridge to facilitate blade changing. Also extending from the main body portion is a flame treatment element for performing a flame treatment operation. The flame treatment element generally comprises a torch or burner. Because both the trimming blade and the flame treatment element are part of the same end effector, the robot simply manipulates the end effector such that the desired one of the trimming blade or the flame treatment element is properly positioned for use. As such, a tooling change can be avoided. While not restricted thereto, it is contemplated that an end effector of the present invention may be used to process vehicle bumper fascias.

A device and method for adjusting the magnetic strength of a magnetic end effector for lift systems is described. The magnetic end effector is capable of lifting discriminate payloads by selectively varying the strength of the magnetic forces output by the magnetic end effector. An actuator can be operatively coupled to the variable strength magnet end effector, wherein the actuator is selectively actuatable to control the adjustment of the variable strength magnet. The actuator may also be configured to maintain the variable strength magnet at a desired magnetic force output strength once achieved for any given amount of time.

A rotary cutting tool, such as a milling cutter (10) includes a central hub (12), a cutting rim (14) and a plurality of spokes (22) connecting the central hub (12) to the cutting rim (14). Each spoke (22) is separated by an opening (32) and polygonal in cross-sectional shape formed by two side walls (22a, 22b), two front walls (22c, 22d) and a rear wall (22e). One of the side walls (22a) of each spoke (22) is formed at a pitch angle (42) with respect to a central axis (11) of the cutting tool (10) that is sufficient to cause lift of chips through the opening (32), thereby providing effective chip evacuation during a material removal operation.

The present invention extends to a disinfection cap for disinfecting a male luer end of an infusion therapy device. The disinfection cap can include an internal reservoir containing an antimicrobial or saline solution which is sealed with a flexible septum to prevent the solution from evaporating. The septum can include one or more slits or pierceable seams that allow a male luer end of an infusion therapy device to be inserted through the septum and into the solution. While the male luer is inserted through the septum, the solution contacts both the inner and outer surfaces of the male luer. Because the septum reduces evaporation of the solution and prevents the solution from leaking out of the cap, the solution remains in contact with the male luer for a longer duration then when typical disinfection caps are used thereby increasing the effectiveness of the disinfectant.

An approach for IR-based metrology for detecting stress and/or defects around TSVs of semiconductor devices is provided. Specifically, in a typical embodiment, a beam of IR light will be emitted from an IR light source through the material around the TSV. Once the beam of IR light has passed through the material around the TSV, the beam will be analyzed using one or more algorithms to determine information about TSV stress and/or defects such as imbedded cracking, etc. In one embodiment, the beam of IR light may be split into a first portion and a second portion. The first portion will be passed through the material around the TSV while the second portion is routed around the TSV. After the first portion has passed through the material around the TSV, the two portions may then be recombined, and the resulting beam may be analyzed as indicated above.

A defect inspection device has: an illumination optical system which irradiates a predetermined region of an inspection target with illumination light; a detection optical system which has a detector provided with a plurality of pixels by which scattered light from the predetermined region of the inspection target due to illumination light from the illumination optical system can be detected; and a signal processing portion which is provided with a correction portion which corrects pixel displacement caused by change in a direction perpendicular to a surface of the inspection target with respect to a detection signal based on the scattered light detected by the detector of the detection optical system, and a defect determination portion which determines a defect on the surface of the inspection target based on the detection signal corrected by the correction portion.

The invention discloses a novel method of controlling the open circuit potential (OCP) of a medical implant by coupling it with small amounts of metals having a lower OCP than the implant. Coupling of Mg to less than 1% of the surface area of a titanium implant is shown to induce cathodic polarization of the titanium that inhibits cell proliferation at the surface of the implant. Mg—Ti coupling in medical devices promises to attenuate or eliminate potential complications of surgery such as peri-implantitis and bacterial infections at the site of implantation.

Compositions and methods for improved delivery of macromolecules into eukaryotic cells are provided. Fusogenic peptides from fusion proteins of non-enveloped viruses enhance the efficiency of transfection of eukaryotic cells mediated by transfection agents such as cationic lipids, polycationic polymers such as PEI and dendrimers. These fusogenic peptides are used as part of a transfection complex that efficiently delivers a macromolecule, for example, a nucleic acid, into a eukaryotic cell. Novel cationic lipids and compositions of cationic lipids also are provided that may be used for the introduction of macromolecules such as nucleic acids, proteins and peptides into a variety of cells and tissues. The lipids can be used alone, in combination with other lipids and/or in combination with fusogenic peptides to prepare transfection complexes.

A method models a defect management routine. Both the modeling and a handling are executed within a manufacturing execution system. During an engineering phase: modeling the production process and creating a library of possible defect types which may occur; assigning the defect types to at least one defect group; creating a library of defect specifications; creating a library of defect type specification details; creating at least one runtime defect criteria that is used to link the defect type to a certain production volume; and creating a runtime defect measurement routine that monitors a corrective measure. During a runtime production phase evaluating the product produced; identifying the respective defect type out of the library of defect types; and using the identified defect type to determine a corrective measure, a runtime defect criteria identifying the resource causing the defect type, a production volume, and to run the respective runtime defect management routine.

A method of controlling an operation of a robotically-controlled surgical instrument can include receiving a first input signal at a controller indicative of a user's readiness to actuate the surgical instrument to perform a surgical procedure, outputting an output signal from the controller to provide feedback to the user in response to the received first input signal, receiving a second input signal at the controller confirming the user's readiness to actuate the surgical instrument, outputting an actuation signal from the controller in response to receiving the second input signal, and actuating the surgical instrument to perform the surgical procedure based on the actuation signal.

Provided herein are novel compounds and novel protected compounds that can be derived from polymyxin, including, e.g., polymyxin A. The novel compounds have antibacterial properties against a diverse range of Gram negative bacteria and reduced toxicity compared to polymyxins such as polymyxin A. Also provided are antibacterial pharmaceutical compositions containing the novel compounds and novel protected compounds, as well as methods for preparing the antibacterial compounds and protected compounds.

Whether the growth hormone (GH)/Insulin-like growth factor 1(IGF-I) axis exerts cardioprotective effects remains controversial; and the underlying mechanism(s) for such actions are unclear. Here we tested the hypothesis that growth-hormone releasing hormone (GHRH) directly activates cellular reparative mechanisms within the injured heart, in a GH/IGF-I independent fashion. Following experimental myocardial infarction (MI), rats were randomly assigned to receive, during a 4 week period, either placebo (n=14), rat recombinant GH (rrGH, n=8) or JI-38 (n=8; 50 μg/Kg/day), a potent GHRH-agonist. JI-38 did not elevate serum levels of GH or IGF-I, but markedly attenuated the degree of cardiac functional decline and remodeling after injury. In contrast, GH administration markedly elevated body weight, heart weight, circulating GH and IGF-I, but did not offset the decline in cardiac structure and function. Whereas, both JI-38 and GH augmented levels of cardiac precursor cell proliferation, only JI-38 increased anti-apoptotic gene expression. The receptor for GHRH was detectable on myocytes supporting direct activation of cardiac signal transduction. Collectively, these findings demonstrate that within the heart GHRH-agonists can activate cardiac repair following MI, suggesting the existence of a potential signaling pathway based on GHRH in the heart. The phenotypic profile of the response to a potent GHRH agonist has therapeutic implications.

Provided herein are novel compounds and novel protected compounds that can be derived from polymyxin, including, e.g., polymyxin A. The novel compounds have antibacterial properties against a diverse range of Gram negative bacteria and reduced toxicity compared to polymyxins such as polymyxin A. Also provided are antibacterial pharmaceutical compositions containing the novel compounds and novel protected compounds, as well as methods for preparing the antibacterial compounds and protected compounds.

A disk drive is disclosed including a disk having a plurality of sectors, and a head actuated over the disk. A defect threshold is initialized, and a first sector is read to generate a first read signal. The first read signal is processed to detect a defect in the first sector relative to the defect threshold. After detecting the defect, the defect threshold is adjusted and the first sector is reread to generate a second read signal. The second read signal is processed to detect the defect in the first sector relative to the adjusted defect threshold.

The present invention provides polymerization processes utilizing an ansa-metallocene catalyst system for the production of olefin polymers. Polymers produced from the polymerization processes have properties that vary based upon the presence or the absence of hydrogen and/or comonomer in the polymerization process.

A multi-layer occluder for treating a target site within the body is provided. The occluder may include first and second layers. For example, the first layer may include braided strands of metallic material, and the second layer may include braided strands of polymeric material. At least one of the first or second layers may be configured to facilitate thrombosis.

Braid-balls suitable for aneurysm occlusion and/or parent vessel occlusion/sacrifice (e.g., in treating neurovascular defects) are disclosed. Especially for aneurysm treatment, but also for either one of the aforementioned treatments, the form of the ball is very important. In particular, the density of the device is paramount in applications where braid itself is intended to moderate or stop blood flow—allowing thrombosis within a volume formed by the ball.

A machined ceramic article having an initial surface defect density and an initial surface roughness is provided. The machined ceramic article is heated to a temperature range between about 1000° C. and about 1800° C. at a ramping rate of about 0.1° C. per minute to about 20° C. per minute. The machined ceramic article is heat-treated in air atmosphere. The machined ceramic article is heat treated at one or more temperatures within the temperature range for a duration of up to about 24 hours. The machined ceramic article is then cooled at the ramping rate, wherein after the heat treatment the machined ceramic article has a reduced surface defect density and a reduced surface roughness.

Material removal tool (100), such as for forming surfaces of valve seats, includes an integral or separable reduced diameter circumferential insert housing (106) including a plurality of inserts (120) bonded thereto. The plurality of inserts (120) include cutting surfaces (122) at different axial and radial positions relative to the axis (112) of the material removal tool (100). Cutting surfaces (122) at different axial and radial positions are arranged at different angles to the axis (112), and at least one cutting surface (122) on at least one insert is at an angle of about 45 degrees relative to the axis (112). Cutting surfaces (122) can be located on one insert-type or different insert-types and can have different combinations of cutting surfaces (122). When arranged circumferentially on the insert housing (106), a N-effective material removal tool (100) is formed. Methods of machining using the N-effective material removal tool (100) is also disclosed.

A method is provided for operating a parking brake module that is at least partially integrated into a compressed air generation system in the event of defects, having a control unit, solenoid valves, and a relay valve for aerating and deaerating at least one spring-loaded brake cylinder. A pressure in the parking brake module which is elevated compared to a normal pressure is determined. A constant compressed air delivery is stopped. A reduced switch-off pressure of the compressed air generation system is set. The pressure level in the parking brake module is lowered to the reduced switch-off pressure through repeated activation of the relay valve.

According to one aspect of the present disclosure, a surgical instrument is disclosed. The instrument includes a handle portion, a body portion extending distally from the handle portion and defining a first longitudinal axis and a loading unit. The loading unit includes a tool assembly, the loading adapted to be coupled to the body portion. The instrument also includes a sensor tube movably positioned within the body portion, the sensor tube adapted to engage the loading unit and a load switch coupled to a microcontroller. The load switch is adapted to be actuated by the sensor tube when the sensor tube is engaged by the loading unit being inserted into the body portion.

The subject invention pertains to matrix metalloproteinase (MMP) inhibitors that exhibit an IC50 of below 10−4M against MMP and have substantially no activity against non-MMP metalloproteinase-related events. The MMP inhibitors of the invention have reduced side-effects, especially with respect to joint pain.