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Inverse Dynamics is used to calculate the forces and moments in the joints of multibody systems investigated in fields such as Biomechanics or Robotics. In a didactic spirit, this paper begins with an overview of the derivations of the kinematical and dynamical equations of rigid bodies from the point of view of modern Continuum Mechanics. Then, it introduces a matrix formulation for the solution of Inverse Dynamics problems and, finally, reports a simple two-dimensional example of application to a problem in Biomechanics.

In this paper we propose a theoretical model including a susceptible-infected-recovered-dead (SIRD) model of epidemic in a dynamic macroeconomic general equilibrium framework with agents' mobility. The latter affect both their income (and consumption) and their probability of infecting and of being infected. Strategic complementarities among individual mobility choices drive the evolution of aggregate economic activity, while infection externalities caused by individual mobility affect disease diffusion. Rational expectations of forward looking agents on the dynamics of aggregate mobility and epidemic determine individual mobility decisions. The model allows to evaluate alternative scenarios of mobility restrictions, especially policies dependent on the state of epidemic. We prove the existence of an equilibrium and provide a recursive construction method for finding equilibrium(a), which also guides our numerical investigations. We calibrate the model by using Italian experience on COVID-19 epidemic in the period February 2020 - May 2021. We discuss how our economic SIRD (ESIRD) model produces a substantially different dynamics of economy and epidemic with respect to a SIRD model with constant agents' mobility. Finally, by numerical explorations we illustrate how the model can be used to design an efficient policy of state-of-epidemic-dependent mobility restrictions, which mitigates the epidemic peaks stressing health system, and allows for trading-off the economic losses due to reduced mobility with the lower death rate due to the lower spread of epidemic.

Cracks in articular cartilage compromise tissue integrity and mechanical properties and lead to chondral lesions if untreated. An understanding of the mechanics of cracked cartilage may help in the prevention of cartilage deterioration and the development of tissue-engineered substitutes. The degeneration of cartilage in the presence of cracks may depend on the ultrastructure and composition of the tissue, which changes with aging, disease and habitual loading. It is unknown if the structural and compositional differences between immature and mature cartilage affect the mechanics of cartilage cracks, possibly predisposing one to a greater risk of degeneration than the other. We used a fibre-reinforced poro-viscoelastic swelling material model that accounts for large deformations and tension-compression non-linearity, and the finite element method to investigate the role of cartilage structure and composition on crack morphology and tissue mechanics. We demonstrate that the crack morphology predicted by our theoretical model agrees well with the histo-morphometric images of young and mature cracked cartilages under indentation loading. We also determined that the crack morphology was primarily dependent on collagen fibre orientation which differs as a function of cartilage depth and tissue maturity. The arcade-like collagen fibre orientation, first discussed by Benninghoff in his classical 1925 paper, appears to be beneficial for slowing the progression of tissue cracks by ‘sealing’ the crack and partially preserving fluid pressure during loading. Preservation of the natural load distribution between solid and fluid constituents of cartilage may be a key factor in slowing or preventing the propagation of tissue cracks and associated tissue matrix damage. Statement of significance Cracks in articular cartilage can be detrimental to joint health if not treated, but it is not clear how they propagate and lead to tissue degradation. We used an advanced numerical model to determine the role of cartilage structure and composition on crack morphology under loading. Based on the structure and composition found in immature and mature cartilages, our model successfully predicts the crack morphology in these cartilages and determines that collagen fibre as the major determinant of crack morphology. The arcade-like Benninghoff collagen fibre orientation appears to be crucial in ‘sealing’ the tissue crack and preserves normal fluid-solid load distribution in cartilage. Inclusion of the arcade-like fibre orientation in tissue-engineered construct may help improve its integration within the host tissue.

Under given prestress conditions, solitary waves in fluid-filled elastic tubes are confined to a rather narrow set of combinations of the background fluid velocity and the wave speed. This set, which we call the domain of existence, is bounded by several curves that represent various physical and mathematical restrictions. Remarkably, these restrictions can be cast as purely algebraic conditions to be imposed upon the governing system of differential equations. Paramount among the physical restrictions are the avoidance of wrinkles and the self-impenetrability of the wave profile. In particular, the existence of a critical wave speed of impending wrinkling, independent of the background fluid velocity, is established rigorously.

In the original paper, we erroneously used the total potential energy (Helmholtz free energy of the material plus potential energy of the external forces) in the entropy inequality.

An alkyl functionalized gellan gum derivative was here used to produce hydrogels containing hydroxyapatite and tricalcium phosphate nanoparticles as injectable nanostructured scaffolds for bone regeneration. The amphiphilic nature of the polysaccharide derivative along with its thermotropic behavior and ionotropic crosslinking features made possible to produce injectable bone mimetic scaffolds that can be used to release viable cells and osteoinductive biomolecules. The influence of different nanoparticles concentration on the rheological and physicochemical properties of the injectable systems was studied. We found that the presence of inorganic nanoparticles reinforces the three-dimensional hydrated polymeric networks without influencing their injectability but improving the physicochemical properties of ionotropic crosslinked hydrogels produced with two different curing media. Preliminary cytocompatibility tests performed with murine preosteoblast cells revealed that gellan gum based hydrogels can safely encapsulate viable cells. Loading and release experiments for Dexamethasone and stromal cell-derived factor-1 demonstrate the drug delivery features of the obtained injectable systems. This article is protected by copyright. All rights reserved.

We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g.\ because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton-Jacobi-Bellman equation identifies with the minimal cost function, provided that the closed-loop equation admits a solution. Conditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of \emph{Regular Lagrangian Flows}. From the applied point of view, we provide a numerical implementation of the model in a case study with quadratic instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small., 17 pages, 4 figures

We propose a model, which nests a susceptible-infected-recovered-deceased (SIRD) model of epidemic into a dynamic macroeconomic equilibrium framework with agents’ mobility. The latter affect both their income and their probability of infecting and being infected. Strategic complementarities among individual mobility choices drive the evolution of aggregate economic activity, while infection externalities caused by individual mobility affect disease diffusion. The continuum of rational forward-looking agents coordinates on the Nash equilibrium of a discrete time, finite-state, infinite-horizon Mean Field Game. We prove the existence of an equilibrium and provide a recursive construction method for the search of an equilibrium(a), which also guides our numerical investigations. We calibrate the model by using Italian experience on COVID-19 epidemic and we discuss policy implications.

In this work, we contribute to the study of the structural reorganisation of biological tissues in response to mechanical stimuli. We specialise our investigation to a class of hydrated soft tissues, whose internal structure features reinforcing fibres. These are oriented statistically within the tissue, and their pattern of orientation is such that, at each material point, the tissue is anisotropic. From its natural, stress-free state, the tissue can be distorted anelastically into a global reference configuration, and then deformed under the action of external mechanical loads. The anelastic distortions are responsible for changing irreversibly the internal structure of the tissue, which, in the present context, occurs through both the rearrangement of the bonds among the tissue cells and the deformation-driven reorientation of the fibres. The anelastic strains, in addition, are assumed to model the onset and evolution of microcracks in the tissue, which may be triggered by the mechanical loads applied to the tissue in the case of traumatic events, or diseases. For our purposes, we formulate an anisotropic model of remodelling and we consider a fully isotropic model of structural reorganisation for comparison, with the aim to study if, how, and to what extent the evolution of anelastic distortions is influenced by the tissue’s anisotropy.

Starting from the observation that the growth of a body breaks the time translation symmetry of the body’s dynamics, we determine a scalar field, called internal time, that defines an indicator of the intrinsic time scale of the growth-related body’s structural evolution. By recasting the theory of growth for monophasic media within a variational framework, we obtain the internal time as the solution of a partial differential equation descending from Noether’s Theorem. We do this by considering two approaches, one formulated in terms of internal variables and one adopting the concept of augmented kinematics.

This study focusses on the remodelling of biological tissues in the framework of the theory of material uniformity. A constitutive evolution model is introduced, including fibre recruitment and reorientation, and subjected to the entropy inequality, which enforces the Second Principle of Thermodynamics. The model is applied to a numerical example describing a pressurised fibre-reinforced cylinder, roughly representing an artery, and is able to capture the major characteristics of remodelling in arteries, as reported in the literature.

We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease's transmission rate is a diffusive stochastic process whose trend can be adjusted via costly confinement policies. We provide a complete theoretical analysis, as well as numerical experiments illustrating the structure of the optimal lockdown policy. In all our experiments the latter is characterized by three distinct periods: the epidemic is first let freely evolve, then vigorously tamed, and finally a less stringent containment should be adopted. Moreover, the optimal containment policy is such that the product "reproduction number x percentage of susceptible" is kept after a certain date strictly below the critical level of one, although the reproduction number is let oscillate above one in the last more relaxed phase of lockdown., MSC2010 subject classification: 93E20, 49N90, 92D30, 97M40

Item does not contain fulltext The aim of the work was to determine the effects of the chemical functionalization of hyaluronic acid (HA) with pendant aliphatic tails at different lengths and free amino groups in terms of chemical reactivity, degradation rate, drug-eluting features, and surface properties when processed as electrospun membranes (EM) evaluating the osteoinductive potential for a possible application as guided bone regeneration (GBR). To this end, a series of HA derivatives with different aliphatic tails (DD-Cx mol% ≈ 12.0 mol%) and decreasing derivatization of free amino groups (DD(EDA) mol% from 70.0 to 30.0 mol%) were first synthesized, namely Hn. Then dexamethasone-loaded Hn EM, i.e. HnX were prepared from aqueous polymeric solutions with polyvinyl alcohol (PVA), as a non-ionogenic linear flexible polymeric carrier, and the multifunctional 2-hydroxypropyl- cyclodextrin (HPCD) which acted as a rheological modifier, a stabilizer of Taylor's cone, and a solubilizing agent. A comprehensive characterization of the membranes was carried out through ATR-IR, XRD, and WCA measurements. According to the in vitro hydrolytic and enzymatic degradation and drug release in different aqueous media for two months, the insertion of alkyl pendant grafts and the crosslinking process provided tuneable additional resistance to the whole membrane suitably for the final application of the membranes. Cell culture showed the cytocompatibility and cell proliferation until 7 days. Osteogenic differentiation and mineralization of pre-osteoblastic MC3T3 cells occurred for most of membranes after 35 days as valued by measuring ALP activity (50 nmol 4-np/h/nf DNA) and the deposition of calcium (120-140 μg ml(-1)).

International audience; We study the joint determination of optimal investment and optimal depollution in a spatiotemporal framework where pollution is transboundary. Pollution is controlled at a global level. The regulator internalizes that: (i) production generates pollution, which is bad for the wellbeing of population, and that (ii) pollution flows across space driven by a diffusion process. We solve analytically for the optimal investment and depollution spatiotemporal paths and characterize the optimal long-term spatial distribution when relevant. We finally explore numerically the variety of optimal spatial distributions obtained using a core/periphery model where the core differs from the periphery either in terms of input productivity, depollution efficiency, environmental awareness or self-cleaning capacity of nature. We also compare the distributions with and without diffusion. Key aspects in the optimal policy of the regulator are the role of aversion to inequality, notably leading to smoothing consumption across locations, and the control of diffusive pollution adding another smoothing engine.

We consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional degenerate singular stochastic control problem is solved by combining techniques of viscosity theory and free boundary problems. We provide a detailed description of the problem's value function and of the geometry of the state space, which is split into three regions by two monotone curves. Our main result shows that those curves are continuously di fferentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary diff erential equations., MSC2010 subject classification: 93E20, 91A55, 49L25, 49J40, 35R35, 91B64

Fluorescence recovery after photobleaching (FRAP) is a widely used technique for studying diffusion in biological tissues. Most of the existing approaches for the analysis of FRAP experiments assume isotropic diffusion, while only a few account for anisotropic diffusion. In fibrous tissues, such as articular cartilage, tendons and ligaments, diffusion, the main mechanism for molecular transport, is anisotropic and depends on the fibre alignment. In this work, we solve the general diffusion equation governing a FRAP test, assuming an anisotropic diffusivity tensor and using a general initial condition for the case of an elliptical (thereby including the case of a circular) bleaching profile. We introduce a closed-form solution in the spatial coordinates, which can be applied directly to FRAP tests to extract the diffusivity tensor. We validate the approach by measuring the diffusivity tensor of [Formula: see text] FITC-Dextran in porcine medial collateral ligaments. The measured diffusion anisotropy was [Formula: see text] (SE), which is in agreement with that reported in the literature. The limitations of the approach, such as the size of the bleached region and the intensity of the bleaching, are studied using COMSOL simulations.

Here, an asymmetric double-layer membrane has been designed and fabricated by electrospinning as a tool for a potential wound healing application. A hydrophobic layer has been produced by using a polyurethane-polycaprolactone (PU-PCL) copolymer and loaded with the antibacterial ciprofloxacin whereas an ion responsive hydrophilic layer has been produced by using an octyl derivative of gellan gum (GG-C8) and polyvinyl alcohol (PVA) and loaded with the growth factor FGF-2. This study investigated how the properties of this asymmetric membrane loaded with actives, were influenced by the ionotropic crosslinking of the hydrophilic layer. In particular, the treatment in DPBS and the crosslinking in CaCl2 0.1 or 1 M of the hydrophilic layer affected the release profile of the bioactive molecules allowing to modulate both the antimicrobial effect, as assayed by logarithmic reduction of the Staphylococcus aureus viable count, and the chemoattractant properties on NIH 3 T3 cell line, as assayed by scratch test and cell chemoattraction assay. © 2021 Elsevier B.V.

In hypoelastic constitutive models, an objective stress rate is related to the rate of deformation through an elasticity tensor. The Truesdell, Jaumann, and Green–Naghdi rates of the Cauchy and Kirchhoff stress tensors are examples of the objective stress rates. The finite element analysis software ABAQUS uses a co-rotational frame which is based on the Jaumann rate for solid elements and on the Green–Naghdi rate for shell and membrane elements. The user subroutine UMAT is the platform to implement a general constitutive model into ABAQUS, but, in order to update the Jacobian matrix in UMAT, the model must be expressed in terms of the Jaumann rate of the Kirchhoff stress tensor. This study aims to formulate and implement various hypoelastic constitutive models into the ABAQUS UMAT subroutine. The developed UMAT subroutine codes are validated using available solutions, and the consequence of using wrong Jacobian matrices is elucidated. The UMAT subroutine codes are provided in the “Electronic Supplementary Material” repository for the user’s consideration.

International audience; In this paper, we revisit the theory of spatial externalities. In particular, we depart in several respects from the important literature studying the fundamental pollution free riding problem uncovered in the associated empirical works. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for air and water pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. In particular, net pollution flows diffuse at an increasing rate as we approach the borders, with strong asymmetries under advection, and structural breaks show up at the borders. We also build a formal case in which a larger number of states goes with the exacerbation of pollution externalities. Finally, we explore how geographic discrepancies affect the shape of the border effects.

Inspired by the seminal works of Eshelby (Philos Trans R Soc A 244A:87–112, 1951, J Elast 5:321–335, 1975) on configurational forces and of Noll (Arch Ration Mech Anal 27:1–32, 1967) on material uniformity, we study a thermoelastic continuum undergoing volumetric growth and in a dynamical setting, in which we call the divergence of the Eshelby stress the Eshelby force. In the classical statical case, the Eshelby force coincides with the negative of the configurational force. We obtain a differential identity for the modified Eshelby stress, involving the torsion of the connection induced by the material isomorphism of a uniform body, which includes, as a particular case, that found by Epstein and Maugin (Acta Mech 83:127–133, 1990). In this identity, the divergence of the modified Eshelby stress with respect to this connection of the material isomorphism takes the name of modified Eshelby force. Moreover, we show that Eshelby’s variational approach (1975) can be used to formulate not only the balance of material momentum, but also the balance of energy. In this case, we find that what we call Eshelby power is the temporal analogue of the Eshelby force, and we obtain a differential identity for the modified Eshelby power. This leads to concluding that the driving force for the process of growth–remodelling is the Mandel stress. Eventually, we find that the relation between the differential identities for the modified Eshelby force and modified Eshelby power represents the mechanical power expended in a uniform body to make the inhomogeneities evolve.

A systematic representation of the fourth-order magnetostriction tensor for all crystal classes is presented, based on the formalism proposed by Walpole ( Proc R Soc Lond Ser A 1984; 391: 149–179). This representation allows the general, unconstrained case, as well as the case in which the magnetostrictive strain is assumed to be isochoric, to be studied. The knowledge of the fourth-order magnetostriction tensor enables the stress-free magnetostrictive strain tensor as well as the scalar strain in a given direction to be calculated.

We provide an optimal growth spatio-temporal setting with capital accumulation and diffusion across space to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. The technology is AK, K being broad capital. The social welfare function is Benthamite. In sharp contrast to the related literature, which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology and population. Both the transitional spatio-temporal dynamics and the asymptotic spatial distributions are computed in closed form. Concerning the latter, we find, among other results, that: (i) due to inequality aversion, the consumption per capital distribution is much flatter than the distribution of capital per capita; (ii) endogenous spillovers inherent in capital spatio-temporal dynamics occur as capital distribution is much less concentrated than the (pre-specified) technological distribution; (iii) the distance to the center (or to the core) is an essential determinant of the shapes of the asymptotic distributions, that is relative location matters.

Building on the celebrated works by Toupin (1963) on non-linear elastic dielectric materials and by Noll (1967) on the theory of material uniformity, we use the method of linear perturbations to obtain a generalised form of the equations of piezoelectricity in the linear regime, i.e., below the ferroelectric threshold. More specifically, in their most general form, the piezoelectric constitutive equations that we obtain include an anelastic strain and an anelastic polarisation, both arising from the intrinsic inhomogeneity of the body and according to the theory of material uniformity. These are distinct from the irreversible strain and polarisation that occur at values of stress and electric field above the ferroelectric threshold. Some of the known standard forms of the piezoelectricity equations are retrieved as particular cases.

Background: Midostaurin (mido) is approved for treatment of FLT3 mutant-positive (FLT3+) acute myeloid leukemia (AML). However, FLT3 mutation is not the only determinant of mido sensitivity. Here we report phosphoprotein signatures which predict response to chemotherapy (chemo) plus mido, and identify active drug targets on potential resistance pathways. Methods: Samples collected at diagnosis, post-treatment and relapse from FLT3+ patients treated with chemo+mido were obtained from the Leukemia Tissue Bank at the Princess Margaret Cancer Centre. Peptides and enriched phosphopeptides from bone marrow (BM) and peripheral blood (PB) mononuclear cells were quantified using liquid chromatography-tandem mass spectrometry. Signatures for BM/PB diagnosis samples were analyzed independently and used to train a classification machine learning algorithm to group patients (n=54) based on response to treatment. Additional features (e.g. genetic mutations) were also analyzed. Kaplan-Meier and Log-Rank test methods were used to assess differential survival between patient groups. To investigate pathways potentially driving resistance to chemo+mido, differential protein phosphorylation indexes were identified through comparison of post-treatment or relapse samples to paired diagnosis samples. To account for population heterogeneity, a filter was applied based on frequency of observation. Activated pathways potentially driving resistance were identified with functional enrichment tools and kinase-substrate enrichment analysis. Statistical significance of enrichment were determined using parametric methods and p-values adjusted for multiple testing using the Benjamini-Hochberg method. Results: Patients positive for a signature consisting of 26 phosphorylation sites showed a markedly longer survival time than negative patients (PB: 269 vs 76 weeks, Log-Rank p=1.30e-05; BM: 241 vs 56, Log-Rank p=2.13e-09). This signature partially overlapped with an ex-vivo signature of response to mido, described previously by Casado et al (Leukemia, 2018). A proteomic signature was also identified, with positive patients showing a longer survival time than negative patients (PB: 330 vs 173 weeks, Log-Rank p=5.0e-04; BM: 460 vs 156, Log-Rank p=5.2e-06). Key, diverging phosphorylation site signatures were identified between patients with refractory disease/early relapse and patients with complete response and no relapse or death within 2 years post-treatment. Pathways with increased activity in post-treatment or relapse specimens were associated with molecular functions such as regulation of cell proliferation, migration, differentiation and anti-apoptosis. Conclusions: We identified phosphoproteomic and proteomic signatures that differentiate survival mediated by response to chemo+mido. While the former was more predictive, both may enable further stratification of FLT3+ AML receiving mido treatment. Drug targets on pathways demonstrating increased activity in relapse/refractory cases may play a role in resistance; this will be determined in follow-up inhibitor studies. Citation Format: Luis Veiga Nobre, Celia Colomina Basanta, Salvatore Federico Pedicona, Arran David Dokal, Andrea Arruda, Ryan Smith, Calum Greenhalgh, Francesca Patella, Pedro Maria Casado-Izquierdo, Bela Wrench, Jane Theaker, Andrew Thompson, Mark D. Minden, John G. Gribben, David James Britton, Pedro Rodriguez Cutillas. Phosphoproteomics reveals active drug targets on pathways of resistance and predicts response to midostaurin plus chemotherapy in FLT3 mutant-positive acute myeloid leukemia [abstract]. In: Proceedings of the AACR-NCI-EORTC Virtual International Conference on Molecular Targets and Cancer Therapeutics; 2021 Oct 7-10. Philadelphia (PA): AACR; Mol Cancer Ther 2021;20(12 Suppl):Abstract nr LBA013.

Background: Midostaurin is approved for FLT3 mutant-positive (FLT3+) acute myeloid leukemia (AML), however efficacy has also been observed in a subpopulation of FLT3 mutant-negative AML, suggesting that FLT3 mutation is not the only determinant conferring midostaurin sensitivity. Casado et al previously described phosphoprotein signatures significantly associated with ex vivo responses to midostaurin in primary AML blasts (Casado et al Leukaemia 2018). In the current study, we tested whether our signatures could group FLT3+ patients based on clinical responses to midostaurin plus chemotherapy. Methods: FLT3+ bone marrow (BM) and peripheral blood (PB) specimens were collected at diagnosis, post-treatment and relapse (n=54 cases) from the Leukemia Tissue Bank at Princess Margaret Cancer Centre. All patients in this study were treated with standard chemotherapy plus midostaurin. Protein/phosphoprotein-signatures for BM and PB samples were analysed independently. Case-studies with multiple post-treatment time-points or relapse events following second line treatments were also analysed. Peptides (proteomics) and enriched phosphopeptides (phosphoproteomics) were quantified using liquid chromatography - tandem mass spectrometry. A classification machine learning (ML) algorithm was trained to group patients based on response to treatment as a function of protein/phosphoprotein-signature status. Other features (e.g. genetic mutations, HSC-transplant) were also analysed. Differential survival analysis between patient groups was carried out with Kaplan-Meier and Log Rank test methods. Pathways upregulated in post-treatment or relapse specimens, particularly from those cases that responded poorly to chemo + midostaurin (i.e. early relapse / refractory disease) were investigated using enrichment statistical methods including kinase-substrate enrichment analysis (KSEA) and gene ontology analysis and identified as potential mechanisms of resistance. Statistical significance of enrichment was determined using parametric methods and p-values adjusted for multiple testing using the Benjamini-Hochberg method. Results: ML models were developed based on the ex-vivo phosphoproteomics signatures described in the Casado et al study, from which we trained a predictive model (model 1). Patients positive for model 1 exhibited a survival probability of 243 weeks, compared to 126 weeks in signature negative patients (averages by geometric mean, Log Rank p = 9.88e-05). As the patients in the current study received chemotherapy, in addition to midostaurin, we identified a new phosphoproteomic signature consisting of 26 phospho-sites which partially overlapped with the ex-vivo signature. Patients positive for this new phosphoproteomic signature showed a markedly longer survival time than negative patients (269 vs 76 weeks, Log Rank p = 1.30e-05 for PB and 241 vs 56, Log Rank p = 2.13e-09 for BM specimens, Table). A proteomic signature was also identified in the current study. Positive patients showed a longer survival time than negative patients (330 vs 173 weeks, Log Rank p = 5.0e-04 for PB and 460 vs 156, Log Rank p = 5.2e-06 for BM specimens, Table), however this was less differentiating than the phosphoproteomic signature. Pathways upregulated in post-treatment or relapse specimens from early relapse or refractory cases were associated with molecular functions such as cell proliferation, anti-apoptosis, non-homologous end-joining, transcriptional regulation, spliceosome and cytoskeleton remodelling. Conclusions: We have identified protein and phosphoprotein signatures with the potential to further stratify AML for midostaurin treatment. Phosphoproteomic signatures differentiated according to response better than the proteomic signatures. Pathways upregulated in relapse/refractory cases may have a role in resistance and this will be determined in follow up studies. Analysis will also be performed on FLT3 mutant-negative cases to validate the signatures and elucidate mechanisms of resistance in this group. Disclosures Veiga Nobre: Kinomica Ltd.: Current Employment. Minden: Astellas: Consultancy. Gribben: Janssen: Honoraria, Research Funding; AZ: Honoraria, Research Funding; Abbvie: Honoraria; BMS: Honoraria; Gilead/Kite: Honoraria; Morphosys: Honoraria; Novartis: Honoraria; Takeda: Honoraria; TG Therapeutics: Honoraria. Britton: Kinomica Ltd.: Current Employment, Current equity holder in publicly-traded company.

We present and apply a theory of one-parameter $C_{0}$ -semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker notion of sequential equicontinuity, we prove the basic results of the classical theory of $C_{0}$ -equicontinuous semigroups: we show that the semigroup is uniquely identified by its generator and we provide a generation theorem in the spirit of the celebrated Hille–Yosida theorem. Then we particularize the theory in some functional spaces and identify two locally convex topologies that allow us to gather—under a unified framework—various notions of $C_{0}$ -semigroups introduced by some authors to deal with Markov transition semigroups. Finally, we apply the results to transition semigroups associated to stochastic differential equations (SDEs).

This paper aims to study a family of deterministic optimal control problems in infinite dimensional spaces. The peculiar feature of such problems is the presence of a positivity state constraint, which often arises in economic applications. To deal with such constraints, we set up the problem in a Banach space with a Riesz space structure (i.e., a Banach lattice) not necessarily reflexive: a typical example is the space of continuous functions on a compact set. In this setting, which seems to be new in this context, we are able to find explicit solutions to the Hamilton-Jacobi-Bellman (HJB) equation associated to a suitable auxiliary problem and to write the corresponding optimal feedback control. Thanks to a type of infinite dimensional Perron-Frobenius Theorem, we use these results to get information about the optimal paths of the original problem. This was not possible in the infinite dimensional setting used in earlier works on this subject, where the state space was an $\mathrm L^2$ space.

The pioneering work by John D. Eshelby in the 1950s and the 1960s on the theory of materials with defects has opened the doors to what today we call configurational mechanics or, in his honour, Eshelbian mechanics. Two of the main results that Eshelby obtained in this field are the use of the elastic energy-momentum tensor to calculate the net force on a defect and the study of materials with inclusions from the geometrical point of view. In Continuum Mechanics, the energy-momentum tensor is now commonly referred to as the Eshelby stress and is the physical quantity that captures the presence of singularities, such as point defects, inclusions, dislocations. In the study of materials with inclusions, Eshelby established a method for the calculation of the strain and stress fields, which entails a fourth-order tensor that relates the strain in the inclusion to the virtual strain (transformation strain or eigenstrain) defining the geometrical misfit between inclusion and matrix. Surprisingly, perhaps, the scientific communities in these two streams of research seem to have had little or no interaction, i.e. virtually all those researchers that have worked in terms of the Eshelby stress have never used the Eshelby fourth-order tensor, and vice versa. To the best of our knowledge, there exists no explicit mathematical relation between the two objects. Therefore, the objective of this paper is to study the relationship between the Eshelby stress and the Eshelby fourth-order tensor within an ellipsoidal inclusion, in the infinitesimal theory of elasticity. Of the three cases that shall be analysed, the first two are commonly referred to as “homogeneous inclusion” and “inhomogeneous inclusion” in the literature, while we refer to the latter as to “general inclusion”, since it describes both the other two as particular cases.

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated quasi-variational inequality. This enables us to characterize the structure of the continuation and action regions and construct an optimal control. Finally, we focus on the linear case, discussing, by a numerical analysis, the sensitivity of the solution with respect to the relevant parameters of the problem.

We construct a spatiotemporal frame for the study of optimal growth under transboundary pollution. Space is continuous and polluting emissions originate in the intensity of use of the production input. Pollution flows across locations following a diffusion process. The objective functional of the economy is to set the optimal production policy over time and space to maximize welfare from consumption, taking into account a negative local pollution externality and the diffusive nature of pollution. Our framework allows for space and time dependent preferences and productivity, and does not restrict diffusion speed to be spaceindependent. This provides a comprehensive setting to analyze pollution diffusion with a close account of geographic heterogeneity. The involved optimization problem is infinite-dimensional. We propose an alternative method for an analytical characterization of the optimal paths and the asymptotic spatial distributions. The method builds on a deep economic concept of pollution spatiotemporal welfare effect, which makes it definitely useful for economic analysis.

International audience; We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asymptotic (optimal) spatial distribution of pollution. We show that optimal emissions will decrease at given location if and only if local productivity is larger than a threshold which depends both on the local pollution absorption capacity and environmental awareness. Furthermore, we numerically explore the relationship between the spatial optimal distributions of production and (asymptotic) pollution in order to uncover possible (geographic) environmental Kuznets curve cases.

We study a problem of optimal investment/consumption over an innite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times corresponding to the jumps of a Poisson process with intensity , is observed at the trading dates, and is partially observed between two dierent trading dates. The problem is a nonstandard mixed discrete/continuous optimal control problem which we face by the dynamic programming approach. When the utility has a general form we prove that the value function is the unique viscosity solution of the HJB equation and, assuming sucient regularity of the value function, we give a verication theorem that describes the optimal investment strategies for the illiquid asset. In the case of power utility, we prove the regularity of the value function needed to apply the verication theorem, providing the complete theoretical solution of the problem. This allows us to perform numerical simulation, so to analyze the impact of time illiquidity in this mixed market and how this impact is aected by the degree

The flux of a certain extensive physical quantity across a surface is often represented by the integral over the surface of the component of a pseudo-vector normal to the surface. A pseudo-vector is in fact a possible representation of a second-order differential form, i.e. a skew-symmetric second-order covariant tensor, which follows the regular transformation laws of tensors. However, because of the skew-symmetry of differential forms, the associated pseudo-vector follows a transformation law that is different from that of proper vectors, and is named after the Italian mathematical physicist Gabrio Piola (1794–1850). In this work, we employ the methods of Differential Geometry and the representation in terms of differential forms to demonstrate how the flux of an extensive quantity transforms from the spatial to the material point of view. After an introduction to the theory of differential forms, their transformation laws, and their role in integration theory, we apply them to the case of first-order transport laws such as Darcy’s law and Ohm’s law.

Path-dependent PDEs (PPDEs) are natural objects to study when one deals with non Markovian models. Recently, after the introduction of the so-called pathwise (or functional or Dupire) calculus (see [15]), in the case of finite-dimensional underlying space various papers have been devoted to studying the well-posedness of such kind of equations, both from the point of view of regular solutions (see e.g. [15, 9]) and viscosity solutions (see e.g. [16]). In this paper, motivated by the study of models driven by path-dependent stochastic PDEs, we give a first well-posedness result for viscosity solutions of PPDEs when the underlying space is a separable Hilbert space. We also observe that, in contrast with the finite-dimensional case, our well-posedness result, even in the Markovian case, applies to equations which cannot be treated, up to now, with the known theory of viscosity solutions., Comment: To appear in the Annals of Probability

We propose a theory of remodelling in fibre-reinforced biological tissues, in which the fibre orientation follows a given probability density. The latter is characterised by variance and mean angle. We claim that the fibres may change their orientation in time, thereby triggering a remodelling process that can be described by the spatiotemporal evolution of the mean angle. This is determined by solving a balance of external and internal generalised forces. We assign the latter ones by establishing a constitutive theory capable of resolving the spatial variability of the fibre mean angle and featuring a free energy density of the Allen–Cahn type. Through numerical simulations, we compare the predictions of our model with the results of another model available in the literature. Finally, we interpret the evolution of the mean angle as the consequence of a symmetry breaking that occurs in the tissue both spontaneously and due to the coupling between remodelling and deformation.

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a Skorohod reflection problem at a suitable boundary surface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems and it is characterized in terms of the family of unique continuous solutions to parameter-dependent nonlinear integral equations of Fredholm type., 39 pages

The purpose of this chapter is to critically review some results that our groups obtained in previous works, which were devoted to the investigation of the elastic properties of composite materials with a statistical distribution of spheroidal inclusions. These studies were motivated by our interest in the description of mechanical properties of fibre-reinforced biological tissues (such as articular cartilage), starting from the internal structure of these tissues. After an introduction to tensor algebra, which defines the notation and clarifies the mathematical framework adopted in the chapter, we present, in a covariant setting inspired by Differential Geometry, Walpole’s representation of isotropic and transversely isotropic second- and fourth-order tensors, along with its properties. Hence, starting from Eshelby’s seminal work on the problem of an inclusion in an infinite matrix, we briefly review the theories developed by Hill, Walpole and Weng for the determination of the overall elasticity tensor of materials with one or more inclusion phases. Then, we discuss in detail the cases of composite materials with aligned spheroidal inclusions and with statistically oriented spheroidal inclusions. Emphasis is put on extending Walpole’s formula to the case of inclusions aligned according to some probability density of orientation, both in the transversely isotropic and the isotropic case.