Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate

The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $\sim N^{22/15}$ and the fluctuations vanish when temperature approaches to the BEC critical temperature.Comment: RevTex, 4 page

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Potts model on recursive lattices: some new exact results

We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths $L_y=2,3,4,5$. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width $L_y=3$ and $L_y=m+2$, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.Comment: 17 pages, 19 figures. v2 typos corrected, title changed and references, acknowledgements and two further original examples added. v3 one further example added. v4 final versio

The Formation and Evolution of Massive Stellar Clusters in IC 4662

We present a multiwavelength study of the formation of massive stellar clusters, their emergence from cocoons of gas and dust, and their feedback on surrounding matter. Using data that span from radio to optical wavelengths, including Spitzer and Hubble ACS observations, we examine the population of young star clusters in the central starburst region of the irregular Wolf-Rayet galaxy IC 4662. We model the radio-to-IR spectral energy distributions of embedded clusters to determine the properties of their HII regions and dust cocoons (sizes, masses, densities, temperatures), and use near-IR and optical data with mid-IR spectroscopy to constrain the properties of the embedded clusters themselves (mass, age, extinction, excitation, abundance). The two massive star-formation regions in IC 4662 are excited by stellar populations with ages of ~ 4 million years and masses of ~ 3 x 10^5 M_sun (assuming a Kroupa IMF). They have high excitation and sub-solar abundances, and they may actually be comprised of several massive clusters rather than the single monolithic massive compact objects known as Super Star Clusters (SSCs). Mid-IR spectra reveal that these clusters have very high extinctions, A_V ~ 20-25 mag, and that the dust in IC 4662 is well-mixed with the emitting gas, not in a foreground screen.Comment: 7 pages, 11 figures, to appear in proceedings of the conference "Young Massive Star Clusters: Initial Conditions and Environments ", held in Granada, Spain, September 200

Structural Phase Transitions and Sodium Ordering in Na0.5CoO2: a Combined Electron Diffraction and Raman Spectroscopy Study

The nonstoichiometric NaxCoO2 system exhibits extraordinary physical properties that correlate with temperature and Na concentration in its layered lattice without evident long-range structure modification when conventional crystallographic techniques are applied. For instance, Na0.7CoO2, a thermodynamically stable phase, shows large thermoelectric power; water-intercalated Na0.33CoO2.1.3H2O is a newly discovered superconductor with Tc ~ 4K, and Na0.5CoO2 exhibits an unexpected charge ordering transition at around Tco ~ 55 K. Recent studies suggest that the transport and magnetic properties in the NaxCoO2 system strongly depend on the charge carrier density and local structural properties. Here we report a combined variable temperature transmission electron microscopy and Raman scattering investigation on structural transformations in Na0.5CoO2 single crystals. A series of structural phase transitions in the temperature range from 80 K to 1000 K are directly identified and the observed superstructures and modulated phases can be interpreted by Na-ordering. The Raman scattering measurements reveal phase separation and a systematic evolution of active modes along with phase transitions. Our work demonstrates that the high mobility and ordering of sodium cations among the CoO2 layers are a key factor for the presence of complex structural properties in NaxCoO2 materials, and also demonstrate that the combination of electron diffraction and Raman spectroscopy measurements is an efficient way for studying the cation ordering and phase transitions in related systems.Comment: 22 pages, 5 figure

Transformation of β-Ni(OH)2to NiO nano-sheets via surface nanocrystalline zirconia coating: Shape and size retention

Shape and size of the synthesized NiO nano-sheets were retained during transformation of sheet-like β-Ni(OH)2to NiO at elevated temperatures via nano-sized zirconia coating on the surface of β-Ni(OH)2. The average grain size was 6.42 nm after 600 °C treatment and slightly increased to 10 nm after 1000 °C treatment, showing effective sintering retardation between NiO nano-sheets. The excellent thermal stability revealed potential application at elevated temperatures, especially for high temperature catalysts and solid-state electrochemical devices

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Outlier detection and classification in sensor data streams for proactive decision support systems

A paper has a deal with the problem of quality assessment in sensor data streams accumulated by proactive decision support systems. The new problem is stated where outliers need to be detected and to be classified according to their nature of origin. There are two types of outliers defined; the first type is about misoperations of a system and the second type is caused by changes in the observed system behavior due to inner and external influences. The proposed method is based on the data-driven forecast approach to predict the values in the incoming data stream at the expected time. This method includes the forecasting model and the clustering model. The forecasting model predicts a value in the incoming data stream at the expected time to find the deviation between a real observed value and a predicted one. The clustering method is used for taxonomic classification of outliers. Constructive neural networks models (CoNNS) and evolving connectionists systems (ECS) are used for prediction of sensors data. There are two real world tasks are used as case studies. The maximal values of accuracy are 0.992 and 0.974, and F1 scores are 0.967 and 0.938, respectively, for the first and the second tasks. The conclusion contains findings how to apply the proposed method in proactive decision support systems