Internal Dynamic Research Articles

The influence of timescales and data injection schemes for reservoir computing using spin-VCSELs

AbstractReservoir computing with photonic systems promises fast and energy efficient computations. Vertical emitting semiconductor lasers with two spin-polarized charge-carrier populations (spin-VCSEL), are good candidates for high-speed reservoir computing. With our work, we highlight the role of the internal dynamic coupling on the prediction performance. We present numerical evidence for the critical impact of different data injection schemes and internal timescales. A central finding is that the internal dynamics of all dynamical degrees of freedom can only be utilized if an appropriate perturbation via the input is chosen as data injection scheme. If the data is encoded via an optical phase difference, the internal spin-polarized carrier dynamics is not addressed but instead a faster data injection rate is possible. We find strong correlations of the prediction performance with the system response time and the underlying delay-induced bifurcation structure, which allows to transfer the results to other physical reservoir computing systems.

(Invited) Benchmarking and Predicting the Risks of Commercial Li-Ion Cells Undergoing Thermal Runaway

The performance of commercial Li-ion batteries increases year after year. New mechanical designs of cells as well as changing electrolyte and active material compositions continually push performance boundaries forward. With such changes, the risks associated with thermal runaway of cells change too and a challenge persists in recording and benchmarking risks to determine whether increased performance comes at the expense of increased risk in the event of thermal runaway. The Battery Failure Databank provides a record of thermal and mass ejection behaviors of past and present commercial cells and provides a valuable resource for benchmarking behaviors and determining the predictability of risks associated with thermal runaway.A Fractional Thermal Runaway Calorimeter (FTRC), developed by the NASA Johnson Space Center in collaboration with the National Renewable Energy Laboratory (NREL), distinctly measures heat emitted from the body of commercial cells and heat that is ejected from the cell. The FTRC also facilitates in-situ high-speed radiography to link phenomena occurring inside the cell with external thermal measurements. The FTRC was used for all tests recorded in the Battery Failure Databank and high-speed radiographs accompany each thermal dataset. Having thermal, mass ejection, and internal dynamics behaviors from hundreds commercial cells under mechanical and thermal abuse conditions facilitates statistical analyses of cell behaviors and evaluation of the efficacy of machine learning methods for predicting risks associated with thermal runaway.Using data from the Battery Failure Databank, the following three topics will be covered in this talk: Correlations between heat generation and mass ejection: The total heat output from cells showed a strong correlation with the quantity of material ejected. An explanation for this based on distinct heat measurements from ejected and non-ejected materials will be discussed. Potential causes of outlier cells that produce exceptionally high heat: Upon conducting numerous repeat tests for each cell, outlier cells that produce exceptionally high quantities of heat were observed. High-speed radiography data revealed that internal dynamic phenomena can lead to extreme variations in thermal and ejection behavior observed externally. The predictability of thermal runaway outcomes using machine learning methods and limited data: With limited data on thermal behavior, mass ejection, and cell specifications, the accuracy of zero- and one-shot approaches to predicting the variation and distribution of heat output during thermal runaway of a new cell type, based on training data in the Battery Failure Databank, will be discussed. The analyses and open-access resources provided with this work are expected to provide a foundation for benchmarking the behavior and predictability of risks associated with thermal runaway of past and present commercial Li-ion cells. In addition to providing a valuable resource for designing safe battery systems, it is expected that this data will be imperative as we evaluate next generation cell designs and assess their respective failure mechanisms and associated risks.

External environment and internal dynamics of “born global”: strategic and operational firm performance

Purpose“Born global firms” are those organizations which, from their inception and by nature, adopt an essentially global-scale entrepreneurial functional and attitudinal strategy for growth. They seek to gain significant competitive advantage by utilizing their internal resources while leveraging external environment potentialities, to sell their outputs internationally. The aim of this research is to investigate the influence of the external business environment and the dynamic capabilities of born global firms, on their strategic and operational performance, as well as the role of leadership vision on their internationalization performance.Design/methodology/approachInitially and resting on extant literature with pertinent foci, including the absorptive capacity and the dynamic capability view theories, a conceptual model is proposed. Subsequently, the model is validated through the partial least square structural equation modeling technique, based on 417 respondents from Indian firms.FindingsThe study concludes that the external business environment and internal dynamic capabilities of born global firms have a significant and positive impact on their strategic, as well as operational performance; with leadership vision playing a significant moderating role to this relationship. The study finally presents the executive implications of the findings and identifies the avenues for further scientific research.Originality/valueThis is a unique study on the topic, both in relation to resources/capabilities versus performance and with regards to the leadership vision's role. It moreover focuses on a primary business force, India, which comprises prime examples of global entrepreneurship. The research constituting a significant contribution to knowledge, as research on how small firms can strategically grow so rapidly and effectively, is still far from conclusive, particularly under the present evolutions that incessantly redefine the contextual business forces upon which strategy is drawn.

Mobile oscillators network with amplification

In this work, we investigate the dynamics of a multilayer network of mobile agents with amplification where each agent is composed of two parts: internal dynamics defined by a Rössler chaotic oscillator and external dynamics defined by the random motion of this agent in 2D space. Each agent characterized by a communication range named ‘vision range’ which is the greatest distance within which two agents can exchange information and therefore establish a coupling. Thus, two cases were studied: the case where only the external dynamic influences the internal dynamic and the case where there is a mutual influence of the internal dynamic on the external dynamic and vice versa. The study of the effects of these parameters leads the internal dynamics of the network to the synchronization (resp. attenuation) and the spatial motion of the agent to the phase synchronization.

Subsonic and supersonic polaron dynamics in polyacetylene

The paper considers the dynamics of a polaron in an electric field on a polyacetylene lattice. The one-electron non-adiabatic approximation based on the Su–Schrieffer–Heeger model is used. In an electric field, a polaron gains one of two saturated velocities, — subsonic and supersonic. Velocity bifurcation occurs in a very narrow range of electric field strengths. In an electric field, the polaron’s internal dynamic and electronic structure changes in a complex way. The supersonic polaron transforms the energy received from the electric field into monochromatic lattice oscillations. The generation of these oscillations is due to the internal polaron dynamics. The effective polaron mass is determined and m* ≈ 1.3. The negative effective mass was also identified. An analysis of the wave function and its phases provides useful information about the polaron evolution. The polaron dynamics is also studied depending on the mode of switching on and off the electric field and in multiple electric fields.

Quantum Tunneling Facilitates Water Motion across the Surface of Phenanthrene.

Quantum tunneling is a fundamental phenomenon that plays a pivotal role in the motion and interaction of atoms and molecules. In particular, its influence in the interaction between water molecules and carbon surfaces can have significant implications for a multitude of fields ranging from atmospheric chemistry to separation technologies. Here, we unveil at the molecular level the complex motion dynamics of a single water molecule on the planar surface of the polycyclic aromatic hydrocarbon phenanthrene, which was used as a small-scale carbon surface-like model. In this system, the water molecule interacts with the substrate through weak O-H···π hydrogen bonds, in which phenanthrene acts as the hydrogen-bond acceptor via the high electron density of its aromatic cloud. The rotational spectrum, which was recorded using chirped-pulse Fourier transform microwave spectroscopy, exhibits characteristic line splittings as dynamical features. The nature of the internal dynamics was elucidated in great detail with the investigation of the isotope-substitution effect on the line splittings in the rotational spectra of the H218O, D2O, and HDO isotopologues of the phenanthrene-H2O complex. The spectral analysis revealed a complex internal dynamic showing a concerted tunneling motion of water involving its internal rotation and its translation between the two equivalent peripheral rings of phenanthrene. This high-resolution spectroscopy study presents the observation of a tunneling motion exhibited by the water monomer when interacting with a planar carbon surface with an unprecedented level of detail. This can serve as a small-scale analogue for water motions on large aromatic surfaces, i.e., large polycyclic aromatic hydrocarbons and graphene.

Study on internal dynamic response during cold start of proton exchange membrane fuel cell with parallel and serpentine flow fields

A deeper understanding of the internal dynamics and transient phenomena during cold start of proton exchange membrane fuel cell (PEMFC) is essential to inspire better strategies. In this study, segmented fuel cell technology is applied to capture the internal current and temperature evolution during cold start of PEMFC. It is found that the effect of flow field on cold start performance is less important than that under normal temperature. The single-channeled serpentine (SS) flow field exhibits the fastest response rate and better cold start performance owing to its high pressure drop and excellent drainage ability. The flow field does not affect the overall evolution trend, but the response rate increases with the pressure drop. During successful cold start, the maximum current density first appears in the downstream of the cathode, then it moves upwards to the middle and inlet region. However, during failed cold start, the current density gradually decreases while moving upstream due to ice blockage. Besides, severe performance degradation occurs after failed cold start. The degradation of the SS flow field is significantly greater than the others, indicating that a rapid response and superior cold start performance may increase the chance of degradation once the cold start fails.

Stellar population of the Rosette Nebula and NGC 2244

Context. Measurements of internal dynamics of young clusters and star-forming regions are crucial to fully understand the process of their formation. A basic prerequisite for this is a well-established and robust list of probable members. Aims. In this work, we study the 2.8° ×2.6° region in the emblematic Rosette Nebula, centred in the young cluster NGC 2244, with the aim of constructing the most reliable candidate member list to date. Using the obtained catalogue, we can determine various structural and kinematic parameters, which can help to draw conclusions about the past and the future of the region. Methods. We constructed a catalogue containing optical to mid-infrared photometry, as well as accurate positions and proper motions from Gaia EDR3 for the sources in the field of the Rosette Nebula. We applied the probabilistic random forest algorithm to derive the membership probability for each source within our field of view. Based on the list of almost 3000 probable members, of which about a third are concentrated within the radius of 20′ from the centre of NGC 2244, we identified various clustered sources and stellar concentrations in the region, and estimated the average distance to the entire region at 1489 ± 37 pc, 1440 ± 32 pc to NGC 2244, and 1525 ± 36 pc to NGC 2237. The masses, extinction, and ages were derived by fitting the spectral energy distribution to the atmosphere and evolutionary models, and the internal dynamic was assessed via proper motions relative to the mean proper motion of NGC 2244. Results. NGC 2244 is showing a clear expansion pattern, with an expansion velocity that increases with radius. Its initial mass function (IMF) is well represented by two power laws (dN/dM ∝ M−α), with slopes α = 1.05 ± 0.02 for the mass range 0.2–1.5 M⊙ and α = 2.3 ± 0.3 for the mass range 1.5–20 M⊙, and it is in agreement with slopes detected in other star-forming regions. The mean age of the region, derived from the HR diagram, is ∼2 Myr. We find evidence for the difference in ages between NGC 2244 and the region associated with the molecular cloud, which appears slightly younger. The velocity dispersion of NGC 2244 is well above the virial velocity dispersion derived from the total mass (1000 ± 70 M⊙) and half-mass radius (3.4 ± 0.2 pc). From the comparison to other clusters and to numerical simulations, we conclude that NGC 2244 may be unbound and that it possibly may have even formed in a super-virial state.

Study of Protein Dynamics via Neutron Spin Echo Spectroscopy.

Most human body proteins' activity and functionality are related to configurational changes of entire subdomains within the protein crystal structure. The crystal structures build the basis for any calculation that describes the structure or dynamics of a protein, most of the time with strong geometrical restrictions. However, these restrictions from the crystal structure are not present in the solution. The structure of the proteins in the solution may differ from the crystal due to rearrangements of loops or subdomains on the pico to nanosecond time scale (i.e., the internal protein dynamics time regime). The present work describes how slow motions on timescales of several tens of nanoseconds can be accessed using neutron scattering. In particular, the dynamical characterization of two major human proteins, an intrinsically disordered protein that lacks a well-defined secondary structure and a classical antibody protein, is addressed by neutron spin echo spectroscopy (NSE) combined with a wide range of laboratory characterization methods. Further insights into protein domain dynamics were achieved using mathematical modeling to describe the experimental neutron data and determine the crossover between combined diffusive and internal protein motions. The extraction of the internal dynamic contribution to the intermediate scattering function obtained from NSE, including the timescale of the various movements, allows further vision into the mechanical properties of single proteins and the softness of proteins in their nearly natural environment in the crowded protein solution.

Analysis of precipitation characteristics in Shanghai based on the visibility graph algorithm

Most of the existing studies on the characteristics of precipitation in Shanghai only focus on the statistical characteristics of the precipitation series rather than the internal dynamic characteristic. The visibility graph algorithm has been proven to be an effective algorithm for grasping the internal dynamics characteristics of time series. Therefore, this paper exploits the visibility graph algorithm to analyze the daily precipitation time series in Shanghai from 2000 to 2020. Some characteristics of precipitation during this period are obtained: Typhoon Mesa and Typhoon Fitow had a profound impact on Shanghai’s precipitation; There is a certain similarity of the precipitation structure in different periods; Only a few nodes in the precipitation network have a profound impact on the precipitation in Shanghai.

Understanding dynamic behavior of proton exchange membrane fuel cell in the view of internal dynamics based on impedance

• Effects of various conditions on transient response of PEM fuel cell are studied. • 2500 Hz impedance and 10 Hz impedance are used to explain voltage response. • Voltage undershoot and overshoot are observed and interpreted. • Charge transfer loss is closely related to oxygen transport and membrane hydration. The transient characteristic of the proton exchange membrane (PEM) fuel cell is an imperative factor for vehicular applications. Currently, a substantial part of previous experimental study regarding the transient response of the PEM fuel cell only focuses on voltage output, while the dynamic internal polarization process is usually ignored. Considering that the electrochemical impedance spectroscopy can represent internal dynamics at different time scales, in this paper, for the first time, in addition to voltage as an indicator of dynamic response performance, the fixed frequency impedance is also applied as an assist signal for voltage response interpretation and internal mechanism analysis. First, a transmission line model is introduced for polarization loss calculation of measured EIS in various conditions. Through quantitative analysis of each polarization loss and each frequency impedance, it is determined that 2500 Hz and 10 Hz impedance can describe the variation trend of proton transfer loss and charge transfer loss, respectively. Based on this, the effects of different step-current, air stoichiometry, backpressure, air humidity, and temperature on the dynamic response of the PEM fuel cell are investigated. Moreover, to fully reveal the internal dynamic mechanism, the transient variation of 2500 Hz and 10 Hz impedance under a broad range of current density is studied. The results indicated that voltage response is strictly related to internal hydration state and oxygen transfer. Especially, poor internal humidification may lead to local starvation. These works offer a more profound understanding of PEM fuel cell transient response, which is significant for system controller design.

Correction to: Intensification and Northward extension of Northwest Pacific anomalous anticyclone in El Niño decaying mid-summer: an energetic perspective

The Northwest Pacific (NWP) anomalous anticyclone (AAC) intensifies and extends northward from El Nino decaying early to mid-summer, despite decaying El Nino-induced sea surface temperature (SST) anomalies in the North Indian Ocean, North Atlantic and subtropical NWP. The present study suggests the intra-seasonal variations of AAC are induced by local mean state changes and investigates the underlying mechanisms from the perspective of energetics. Compared with early summer, the efficiency of dry energy conversion from the mean flow to El Nino-excited AAC pattern increases in El Nino decaying mid-summer. The moist feedback over subtropical NWP is also enhanced in El Nino decaying mid-summer due to the onset of the climatological NWP summer monsoon. Both of them contribute to the intensification of El Nino-excited AAC pattern. Moreover, mean state changes over East Asia–NWP from early to mid-summer are found in favor of the northward shift of the preferred latitude of the circulation anomalies. Thus, the El Nino-excited AAC pattern are more northward-extended in El Nino decaying mid-summer. Empirical orthogonal function analyses further confirm that the northward extension of El Nino-excited AAC pattern stems from changes of local internal dynamic mode. The present study highlights that both the El Nino-induced SST anomalies and local atmospheric internal dynamics are of paramount importance for the intra-seasonal variations of AAC in El Nino decaying summer.

Intensification and Northward extension of Northwest Pacific anomalous anticyclone in El Niño decaying mid-summer: an energetic perspective

The Northwest Pacific (NWP) anomalous anticyclone (AAC) intensifies and extends northward from El Niño decaying early to mid-summer, despite decaying El Niño-induced sea surface temperature (SST) anomalies in the North Indian Ocean, North Atlantic and subtropical NWP. The present study suggests the intra-seasonal variations of AAC are induced by local mean state changes and investigates the underlying mechanisms from the perspective of energetics. Compared with early summer, the efficiency of dry energy conversion from the mean flow to El Niño-excited AAC pattern increases in El Niño decaying mid-summer. The moist feedback over subtropical NWP is also enhanced in El Niño decaying mid-summer due to the onset of the climatological NWP summer monsoon. Both of them contribute to the intensification of El Niño-excited AAC pattern. Moreover, mean state changes over East Asia–NWP from early to mid-summer are found in favor of the northward shift of the preferred latitude of the circulation anomalies. Thus, the El Niño-excited AAC pattern are more northward-extended in El Niño decaying mid-summer. Empirical orthogonal function analyses further confirm that the northward extension of El Niño-excited AAC pattern stems from changes of local internal dynamic mode. The present study highlights that both the El Niño-induced SST anomalies and local atmospheric internal dynamics are of paramount importance for the intra-seasonal variations of AAC in El Niño decaying summer.

Dynamics of proteins with different molecular structures under solution condition

Incoherent quasielastic neutron scattering (iQENS) is a fascinating technique for investigating the internal dynamics of protein. However, low flux of neutron beam, low signal to noise ratio of QENS spectrometers and unavailability of well-established analyzing method have been obstacles for studying internal dynamics under physiological condition (in solution). The recent progress of neutron source and spectrometer provide the fine iQENS profile with high statistics and as well the progress of computational technique enable us to quantitatively reveal the internal dynamic from the obtained iQENS profile. The internal dynamics of two proteins, globular domain protein (GDP) and intrinsically disordered protein (IDP) in solution, were measured with the state-of-the art QENS spectrometer and then revealed with the newly developed analyzing method. It was clarified that the average relaxation rate of IDP was larger than that of GDP and the fraction of mobile H atoms of IDP was also much higher than that of GDP. Combined with the structural analysis and the calculation of solvent accessible surface area of amino acid residue, it was concluded that the internal dynamics were related to the highly solvent exposed amino acid residues depending upon protein’s structure.

Observer-based consensus control of multi-agent linear parameter varying systems

The state consensus of linear parameter–varying (LPV) agents with observer-based controller is addressed. Multi-agent systems with different LPV dynamics and same dimensions can be considered by the proposed method. The focus is on heterogeneous LPV agents with different dynamics and same dimensions, or identical dynamics but with different parameters. Design procedures are proposed to determine the coupling gains of heterogeneous LPV agents based on linear matrix inequalities. In order to reach consensus, internal dynamics are used in a way that each agent tries to track its corresponding internal dynamic and subsequently, the internal dynamics attempt to reach consensus. All these actions happen in the presence of the communication graph. Unlike the previous methods, no restrictive assumptions are considered on the LPV system matrix of each agent and less assumptions on LPV systems are needed, which make the results of the paper more general. Verifying simulations are provided in order to show the results are successful.

Recurrence Behavior Statistics of Blast Furnace Gas Sensor Data in Industrial Internet of Things

Blast furnace gas (BFG) produced from steel industries is generally one of the most important energy supplies in enterprises. Due to a great deal of output, fluctuation, and heterogeneity in data, it is very difficult to provide profound insights into its internal dynamic. In this article, a novel analysis framework is developed for the BFG data processing, considering the recurrence plot (RP) and the recurrence quantification analysis (RQA). The specific aim is to investigate the relationship between BFG output and its potential influencing factors. This framework can be deemed as a uniform and consistent system with functional components of qualitative visualization and quantitative analysis. Concretely, the BFG outputs related to five factors are separately projected to high-dimensional spaces, followed by that their internal dynamics can be embodied through a 2-D recurrence representation of states. Finally, five RQA parameters are used to quantify the influence of these factors on the BFG output. This is the first attempt revealing the relations among the BFG data from the qualitative and quantitative perspectives. The experimental results show that RP can discover the BFG output patterns of laminar state, chaos, and instability over given three states of influencing factors, and the ranked influential degree can be given by a two-stage standard deviation of all considered RQA measures. Besides, we also demonstrate that the temperature of the hot-blast stove is most relevant to the BFG output, while the influence of considered other factors directly depends on the selected series length.

Quantitative Analysis of AC/DC Side Harmonic Transfer Characteristics for Modular Multilevel Converter and Suppression Measures

MMC (Modular Multilevel Converter) is the preferred topology for renewable energy delivery, but renewable energy resources, such as wind farms, contains much harmonic components. Compared with two-level VSC (Voltage Source Converter), the internal dynamic characteristics of MMC have great impact on the harmonic transmission. This paper quantitatively analyzes the harmonic transferring mechanism from one side to the other side of MMC, and deduces the time-domain analytical expression of the harmonic response on the MMC’s other side. Firstly, the influence of background harmonic on MMC’s control system and electrical system are quantitatively analyzed. On this basis, the equivalent circuit of MMC’s electrical system considering its internal dynamics is established to accurately calculate the effect of background harmonic on the MMC’s other side. In addition, the harmonic transferring impedance in frequency-domain is also defined in this paper, based on that the influence of background harmonic on the MMC’s other side can be calculated quickly. According to the harmonic transferring characteristics analyzed above, a zero-sequence virtual damping strategy is proposed for the first time to suppress the background harmonic transferring. Finally, a 232-level 500kV MMC simulated model is built in MATLAB/Simulink to verify the accuracy of the harmonic transferring calculation method and the effectiveness of the virtual damping suppression strategy.

Interaction of Sea-Level Pulses With Periodically Retreating Barrier Islands

Barrier deposits preserved on continental shelf seabeds provide a record of the paleocoastal environment from the last glacial maximum through the Holocene. The formation of these offshore deposits is often attributed to intermittent periods of rapidly rising sea levels, especially glacial meltwater pulses, which are expected to lead to partial or complete drowning—overstepping—of migrating barrier islands. However, recent cross-shore modeling and field evidence suggests that even for constant sea-level rise and shelf slope, the internal dynamics of migrating barriers could plausibly drive periodic retreat accompanied by autogenic partial overstepping and deposition of barrier sediment. We hypothesize that the interaction of periodic retreat with changes in external (allogenic) forcing from sea-level rise may create novel retreat responses and corresponding relict barrier deposits. Specifically, we posit that autogenic deposits can be amplified by an increased rate of sea-level rise, while in other cases internal dynamics can disrupt or mask the production of allogenic deposits. Here, we model barriers through a range of autogenic-allogenic interactions, exploring how barriers with different inherent autogenic periods respond to discrete, centennial-scale sea-level-rise pulses of variable magnitude and timing within the autogenic transgressive barrier cycle. Our results demonstrate a diversity of depositional signals, where production of relict sands is amplified or suppressed depending on both the barrier’s internal dynamic state and the pulse magnitude. We also show that millennial-scale autogenic periodicity renders barriers vulnerable to complete drowning for relatively low pulse rates of rise (< 15 mm/yr).

Rethinking the Iranian Islamic Revolution of 1979 with the Security Dilemma of the Cold War

The case of Iranian Revolution can be interpreted in different ways in the light of the fact that it isstill a revolution that continues to be written and discussed too much about. The study of the IranianRevolution in literature, in general, confronts a growing resistance with the influence of the oppositionpeople who oppose the oppression of the Pahlavi Dynasty dictatorship and grows under the influence ofthe Islamic phenomenon. However, in order to understand the Iranian Revolution, the perspective thatis focused on the internal dynamics will not be sufficient. The external dynamics and the interactionof external dynamics with these actors must be a further perspective that needs to be focused tounderstand this particular revolution.In this article, the differences of the Iranian Revolution are evaluated in a different perspective fromthe point of view of the literature. Rather than explaining the revolution with the historical process, itfocused on the external dynamics that constitute the historical process. While evaluating the externaldynamics, it is explained that the anarchy created by the Cold War in the international system throughthe security dilemma, and that the internal dynamic effect of this dilemma in a strategic country suchas Iran could be realized by developing the anti-imperialist identity building of Khomeini throughdiscourse and integrating all opposition groups. While evaluating the external dynamics, it is explainedthat the anarchy created by the Cold War in the international system through the security dilemma, andthat the internal dynamic effect of this dilemma in a strategic country such as Iran could be realizedby developing the Anti-Imperialist identity building of Khomeini through discourse and realizing theIslamic revolution of all opposition groups.

Vitamin D can be used as a supplement against cancer stem cells

Cancer is standing like a bottomless pit or a black hole in front of mankind. Scientists are trying all possible ways to find a solution against to cancer. As known, cancer is a phenomenon fed from internal dynamics. One of internal dynamic is cancer stem cells that are involved in the formation and development of cancer. Because of these dynamics, scientists began to search solution inside of the body. Another internal dynamic is vitamin D and it is not only important in calcium homeostasis but also it is important for cell proliferation, differentiation, and apoptosis. In this study, we investigated the effect of vitamin D on cancer stem cells that sorted from MCF-7 cell line and on HEK293 cell line as control. Our results showed that calcitriol treatment reduced the number of CSC (Cancer Stem Cell) in the MCF-7 cell while increased in HEK293 cell population. Gene expression analyses showed that effect of calcitriol on apoptosis plays an important role in this reduction. Deficiency or unavailability of vitamin D may take a role in the pathogenesis of breast cancer.