**2. Experimental**

**2. Experimental**  The samples used in our works were mostly *c*-axis oriented YBCO thin films and GdBCO coated conductors. The *c*-axis oriented YBCO thin films were fabricated by a pulsed laser deposition (PLD) technique on (100) surface of SrTiO3 single crystal substrates. The thickness of the films was about 300 nm. The GdBCO coated conductor, on the other hand, was fabricated on an ion-beam-assisted deposition (IBAD) substrate by a PLD method (Fujikura Ltd., Tokyo, Japan). The thickness of GdBCO layer is 2.2 µm and the self-field critical current *I*c of this tape with 5 mm width is about 280 A. The samples were cut from the tape of the GdBCO coated conductor. The Ag stabilizer layer on the superconducting layer was removed by a chemical process. The YBCO thin films and the samples cut from the GdBCO coated conductor were patterned into a shape of about 40 The samples used in our works were mostly *c*-axis oriented YBCO thin films and GdBCO coated conductors. The *c*-axis oriented YBCO thin films were fabricated by a pulsed laser deposition (PLD) technique on (100) surface of SrTiO3 single crystal substrates. The thickness of the films was about 300 nm. The GdBCO coated conductor, on the other hand, was fabricated on an ion-beam-assisted deposition (IBAD) substrate by a PLD method (Fujikura Ltd., Tokyo, Japan). The thickness of GdBCO layer is 2.2 µm and the self-field critical current *I*c of this tape with 5 mm width is about 280 A. The samples were cut from the tape of the GdBCO coated conductor. The Ag stabilizer layer on the superconducting layer was removed by a chemical process. The YBCO thin films and the samples cut from the GdBCO coated conductor were patterned into a shape of about 40 µm wide and 1 mm long micro-bridge before the irradiation.

µm wide and 1 mm long micro-bridge before the irradiation. The heavy-ion irradiations with Xe ions were performed using the tandem accelerator of JAEA in Tokai, Japan. Tuning of the discontinuity of CDs along the *c*-axis can be controlled by the irradiation energy. The values of *S*e for the Xe-ion irradiation energies above 200 MeV are above 2.9 keV/Å, which is above the threshold value of *S*e = 20 keV/nm to create continuous CDs along the *c*-axis over the whole sample thickness for YBCO [17]. pletely.

Thus, the irradiation with 200 MeV Xe ions was performed to install continuous CDs into YBCO thin films. In addition, the Xe-ion irradiation with 270 MeV was applied in order to create continuous CDs for GdBCO coated conductors, where the projectile length was longer than the thickness of 2.2 µm. Discontinuous CDs, on the other hand, were formed into YBCO thin films and GdBCO coated conductors by the irradiation with 80 MeV Xe ions, where the value of *S*e is below 20 keV/nm: the radius of CDs strongly fluctuates along the ion path and CDs are shortly segmented at intervals in their longitudinal direction when the *S*e is lower than the threshold value, as shown in Figure 3 [19,20,25]. All of the irradiation energies used in our works are enough for the projectile ranges to exceed the thickness of the samples: the incident ions pass through the superconducting layer completely. irradiation directions. The fluence of the irradiation is often represented as a matching field *B*φ: *B*φ is the magnetic field where the density of flux lines is equal to that of CDs, e.g., the fluence of 4.84 × 1010 ions/cm2 corresponds to *B*φ = 1 T. It should be noted that the introduction of irradiation defects causes a lattice distortion of the host matrix, which affects the superconducting properties such as critical temperature (*T*c). The strain induces the oxygen vacancies [26], resulting in the reduction of *T*c: the value of *T*c decreases when the fluence of the irradiation increases [24]. The strain also affects the *J*c properties through the influence on *T*c: *J*c decreases largely, when the influence of the strain increases excessively. Therefore, the irradiation fluences were adjusted to avoid heavy damage to the crystallinity in our works.

The direction of CDs was adjusted by controlling the incident ion beam direction tilted off the *c*-axis by *θ*i, which was always directed perpendicular to the bridge direction of the sample (see Figure 4). When the irradiation directions are dispersed, the fluence in each irradiation direction is calculated by dividing the total fluence by the number of the

The heavy-ion irradiations with Xe ions were performed using the tandem accelerator of JAEA in Tokai, Japan. Tuning of the discontinuity of CDs along the *c*-axis can be controlled by the irradiation energy. The values of *S*e for the Xe-ion irradiation energies above 200 MeV are above 2.9 keV/Å, which is above the threshold value of *S*e = 20 keV/nm to create continuous CDs along the *c*-axis over the whole sample thickness for YBCO [17]. Thus, the irradiation with 200 MeV Xe ions was performed to install continuous CDs into YBCO thin films. In addition, the Xe-ion irradiation with 270 MeV was applied in order to create continuous CDs for GdBCO coated conductors, where the projectile length was longer than the thickness of 2.2 µm. Discontinuous CDs, on the other hand, were formed into YBCO thin films and GdBCO coated conductors by the irradiation with 80 MeV Xe ions, where the value of *S*e is below 20 keV/nm: the radius of CDs strongly fluctuates along the ion path and CDs are shortly segmented at intervals in their longitudinal direction when the *S*e is lower than the threshold value, as shown in Figure 3 [19,20,25]. All of the irradiation energies used in our works are enough for the projectile ranges to exceed the thickness of the samples: the incident ions pass through the superconducting layer com-

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 4 of 22

**Figure 3.** Cross-sectional TEM images of GdBCO coated conductors irradiated with (**a**) 270 MeV and (**b**) 80 MeV Xe ions, respectively. The irradiation dose is 1.94 × 1011 ions/cm2. The arrows indicate several ion tracks. Reprinted with permission from [25], copyright 2015 by IEEE. **Figure 3.** Cross-sectional TEM images of GdBCO coated conductors irradiated with (**a**) 270 MeV and (**b**) 80 MeV Xe ions, respectively. The irradiation dose is 1.94 × 1011 ions/cm2 . The arrows indicate several ion tracks. Reprinted with permission from [25], copyright 2015 by IEEE.

The direction of CDs was adjusted by controlling the incident ion beam direction tilted off the *c*-axis by *θ*i , which was always directed perpendicular to the bridge direction of the sample (see Figure 4). When the irradiation directions are dispersed, the fluence in each irradiation direction is calculated by dividing the total fluence by the number of the irradiation directions. The fluence of the irradiation is often represented as a matching field *B*ϕ: *B*ϕ is the magnetic field where the density of flux lines is equal to that of CDs, e.g., the fluence of 4.84 × 1010 ions/cm2 corresponds to *B*ϕ = 1 T. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 5 of 22

**Figure 4.** Sketch of the experimental arrangement in this work. **Figure 4.** Sketch of the experimental arrangement in this work.

The cross sections of the irradiated samples were observed by conventional transmission electron microscopy (TEM) with a JEM-2000 EX instrument (JEOL, Tokyo, Japan) operating at 200 kV. The thin TEM specimens were prepared by a focused ion beam method using an Quanta 3D system (FEI, Hillsboro, Oregon, USA). The *J*c properties were meas-It should be noted that the introduction of irradiation defects causes a lattice distortion of the host matrix, which affects the superconducting properties such as critical temperature (*T*c). The strain induces the oxygen vacancies [26], resulting in the reduction of *T*c: the value of *T*c decreases when the fluence of the irradiation increases [24]. The strain also affects the *J*c properties through the influence on *T*c: *J*c decreases largely, when the influence

ured through the transport properties by using a four-probe method. The *J*c was defined

field angular dependences of *J*c were evaluated as a function of the angle *θ* between the

Heavy-ion irradiation can introduce CDs in any direction in a controlled manner, so we can install CDs at the magnetic field angles where the *J*c shows a minimum, one by one: the material processing with heavy-ions is one of effective ways to modify the *J*c anisotropy in high-*T*c superconductors, which enables us to push up overall *J*c, as shown in

**Figure 5.** Schematic image of modification of the *J*c anisotropy by controlling the irradiation directions ((**a**) typical *J*c anisotropy of unirradiated high-*T*c superconductors, (**b**) modified *J*c anisotropy

We first examined the influence of bimodal angular distribution of CDs consisting of CDs crossing at ±*θ*i relative to the *c*-axis on the *J*c properties in a wide magnetic field

with CDs along the *c*-axis, (**c**) modified *J*c anisotropy with direction-dispersed CDs).

*3.1. Modification of Jc Around B || c by Controlling Heavy-Ion Irradiation Angles*

magnetic field and the *c*-axis of the samples (see Figure 4).

**3. Results and Discussion**

Figure 5.

of the strain increases excessively. Therefore, the irradiation fluences were adjusted to avoid heavy damage to the crystallinity in our works. The cross sections of the irradiated samples were observed by conventional transmission electron microscopy (TEM) with a JEM-2000 EX instrument (JEOL, Tokyo, Japan) op-

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 5 of 22

**Figure 4.** Sketch of the experimental arrangement in this work.

The cross sections of the irradiated samples were observed by conventional transmission electron microscopy (TEM) with a JEM-2000 EX instrument (JEOL, Tokyo, Japan) operating at 200 kV. The thin TEM specimens were prepared by a focused ion beam method using an Quanta 3D system (FEI, Hillsboro, Oregon, USA). The *J*c properties were measured through the transport properties by using a four-probe method. The *J*c was defined by a criterion of electric field, 1 µV/cm. The transport current was always perpendicular to the magnetic field and the *c*-axis (maximum Lorentz force configuration). The magnetic field angular dependences of *J*c were evaluated as a function of the angle *θ* between the magnetic field and the *c*-axis of the samples (see Figure 4). erating at 200 kV. The thin TEM specimens were prepared by a focused ion beam method using an Quanta 3D system (FEI, Hillsboro, Oregon, USA). The *J*c properties were measured through the transport properties by using a four-probe method. The *J*c was defined by a criterion of electric field, 1 µV/cm. The transport current was always perpendicular to the magnetic field and the *c*-axis (maximum Lorentz force configuration). The magnetic field angular dependences of *J*c were evaluated as a function of the angle *θ* between the magnetic field and the *c*-axis of the samples (see Figure 4). **3. Results and Discussion**

#### **3. Results and Discussion** *3.1. Modification of Jc Around B || c by Controlling Heavy-Ion Irradiation Angles*

#### *3.1. Modification of Jc Around B || c by Controlling Heavy-Ion Irradiation Angles* Heavy-ion irradiation can introduce CDs in any direction in a controlled manner, so

Heavy-ion irradiation can introduce CDs in any direction in a controlled manner, so we can install CDs at the magnetic field angles where the *J*c shows a minimum, one by one: the material processing with heavy-ions is one of effective ways to modify the *J*c anisotropy in high-*T*c superconductors, which enables us to push up overall *J*c, as shown in Figure 5. we can install CDs at the magnetic field angles where the *J*c shows a minimum, one by one: the material processing with heavy-ions is one of effective ways to modify the *J*c anisotropy in high-*T*c superconductors, which enables us to push up overall *J*c, as shown in Figure 5.

**Figure 5.** Schematic image of modification of the *J*c anisotropy by controlling the irradiation directions ((**a**) typical *J*c anisotropy of unirradiated high-*T*c superconductors, (**b**) modified *J*c anisotropy with CDs along the *c*-axis, (**c**) modified *J*c anisotropy with direction-dispersed CDs). **Figure 5.** Schematic image of modification of the *J*c anisotropy by controlling the irradiation directions ((**a**) typical *J*c anisotropy of unirradiated high-*T*c superconductors, (**b**) modified *J*c anisotropy with CDs along the *c*-axis, (**c**) modified *J*c anisotropy with direction-dispersed CDs).

We first examined the influence of bimodal angular distribution of CDs consisting of CDs crossing at ±*θ*i relative to the *c*-axis on the *J*c properties in a wide magnetic field We first examined the influence of bimodal angular distribution of CDs consisting of CDs crossing at ±*θ*i relative to the *c*-axis on the *J*c properties in a wide magnetic field angular range [27,28]. Figure 6 shows the magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs, which were installed by 200 MeV Xe ion irradiation with *B*ϕ = 2 T (c10-2: *θ*i = ±10◦ , c25-2: *θ*i = ±25◦ , c45-2: *θ*i = ±45◦ , p06-2: parallel CD configuration of *θ*i = 6◦ , and Pure: unirradiated samples). The magnetic field was rotated in the splay plane where the two parallel CD families are crossing each other, as shown in Figure 4. All the irradiated samples show an additional peak of the normalized *J*c around *B* || *c* (*θ* = 0◦ ) for lower magnetic fields: the values of the normalized *J*c are enhanced around *B* || *c* compared to the unirradiated one. This indicates that CDs with any crossing angle work as effective PCs, pushing up the *J*c around *B* || *c*. The influence of the crossing angle of CDs is evident in the shape of the additional peak around *B* || *c*: the width of the normalized *J*c peak becomes broader when the crossing angle is larger. Therefore, the bimodal angular distribution of CDs can expand the magnetic field angular range where the normalized *J*c increases, by controlling the crossing angle.

the crossing angle.

**Figure 6.** Magnetic field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs (c10-2: *θ*i = ±10°, c25-2: *θ*i = ±25°, c45-2: *θ*i = ±45°, p06-2: parallel CD configuration of *θ*i = 6°, and Pure: unirradiated samples). Reprinted with permission from [28], copyright 2016 by IOP. **Figure 6.** Magnetic field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs (c10-2: *θ*i = ±10◦ , c25-2: *θ*i = ±25◦ , c45-2: *θ*i = ±45◦ , p06-2: parallel CD configuration of *θ*i = 6◦ , and Pure: unirradiated samples). Reprinted with permission from [28], copyright 2016 by IOP.

angular range [27,28]. Figure 6 shows the magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs, which were installed by 200 MeV Xe ion irradiation with *B*φ = 2 T (c10-2: *θ*i = ±10°, c25-2: *θ*i = ±25°, c45-2: *θ*i = ±45°, p06-2: parallel CD configuration of *θ*i = 6°, and Pure: unirradiated samples). The magnetic field was rotated in the splay plane where the two parallel CD families are crossing each other, as shown in Figure 4. All the irradiated samples show an additional peak of the normalized *J*c around *B* || *c* (*θ* = 0°) for lower magnetic fields: the values of the normalized *J*c are enhanced around *B* || *c* compared to the unirradiated one. This indicates that CDs with any crossing angle work as effective PCs, pushing up the *J*c around *B* || *c*. The influence of the crossing angle of CDs is evident in the shape of the additional peak around *B* || *c*: the width of the normalized *J*c peak becomes broader when the crossing angle is larger. Therefore, the bimodal angular distribution of CDs can expand the magnetic field angular range where the normalized *J*c increases, by controlling

It is noteworthy that the crossover phenomenon from the broad-plateau-like behavior to the double peak emerges on the normalized *J*c around *B* || *c* for c45-2 when the magnetic field increases across the matching field of *B*φ = 2 T: the normalized *J*c more rapidly reduces at *B* || *c* with increasing magnetic field, which results in a dip structure at *B* || *c* for c45-2 at 2 T, as shown in Figure 6. In general, the *J*c peak in the magnetic field angular dependence of *J*c is a sign of long-axis correlated flux pinning of CDs. Their-longaxis correlated flux pinning is maintained up to higher magnetic fields [29,30]. For the crossing angle of *θ*i = ±45°, by contrast, the influence of the long-axis correlated flux pinning is weakened at *B* || *c*, since the directions of CDs are far from the *c*-axis direction. It is noteworthy that the crossover phenomenon from the broad-plateau-like behavior to the double peak emerges on the normalized *J*c around *B* || *c* for c45-2 when the magnetic field increases across the matching field of *B*ϕ = 2 T: the normalized *J*c more rapidly reduces at *B* || *c* with increasing magnetic field, which results in a dip structure at *B* || *c* for c45-2 at 2 T, as shown in Figure 6. In general, the *J*c peak in the magnetic field angular dependence of *J*c is a sign of long-axis correlated flux pinning of CDs. Their-long-axis correlated flux pinning is maintained up to higher magnetic fields [29,30]. For the crossing angle of *θ*i = ±45◦ , by contrast, the influence of the long-axis correlated flux pinning is weakened at *B* || *c*, since the directions of CDs are far from the *c*-axis direction. Thus, the dip behavior at *B* || *c* is a sign of disappearance of their-long axis correlated flux pinning at *B* || *c*.

The effective magnetic field angular region for flux pinning of CDs is described by a trapping angle *ϕt* , at which flux lines begin to be partially trapped by CDs [4]. The general formula of *ϕt* is expressed as:

$$
\varphi\_l = \sqrt{2\,\varepsilon\_p/\varepsilon\_l} \tag{1}
$$

where *εp* is the pinning energy of CDs and *εl* is the line tension of flux lines. The line tension energy of flux lines in anisotropic superconductors is given by the following equation:

$$
\varepsilon\_l(\Theta) \propto \varepsilon\_0 / \gamma^2 \varepsilon(\Theta)^3 \tag{2}
$$

where Θ is the angle between the magnetic field and the *ab*-plane, *ε*0 is a basic energy scale, *γ* is the mass anisotropy, and *ε*(Θ) = (sin2Θ + *γ* −2 cos2Θ) 1/2 [4]. The trapping angle *ϕt* is experimentally estimated as the difference in the angle between the peak value and the minimum one on the magnetic field angular dependence of *J*c [31]. For p06-2, the

value of *ϕt* is ~55◦ at *B* < *B*ϕ, which is estimated from Figure 6a. Using this value of *ϕt* as the trapping angle of CDs parallel to the *c*-axis approximately and *γ* = 5 together with equations (1) and (2), the value of *ϕt* for CDs tilted at *θ*i = 45◦ is about 37◦ . Therefore, CDs tilted at *θ*i = 45◦ hardly contribute to trapping flux lines at *B* || *c*: CDs tilted at *θ*i = 45◦ does not work as their-long-axis correlated PCs for *B* || *c*.

The bimodal angular distribution of CDs for *θ*i ±45◦ gives rise to the drop in *J*c at the mid-direction of the crossing angle. Secondly, we investigated the flux pinning properties for a trimodal angular distribution of CDs consisting of CDs crossing at *θ*i = 0◦ and ±45◦ (referred to as the "standard" trimodal-configuration), in order to obtain high *J*c with no drop over a wide magnetic field angular region [32]. In addition, another geometry for the trimodal configuration was prepared, where a splay plane defined by the three irradiation angles is parallel to the transport current direction (referred to as "another" trimodalconfiguration), as shown in Figure 7: the two trimodal configurations enable us to elucidate the influence of the splay plane direction on the *J*c properties directly. Figure 8 shows the magnetic field angular dependence of normalized *J*c by *J*c0 (= *j*c) at several magnetic fields from 1 T up to 5 T for YBCO thin films with the trimodal angular configurations of CDs. A large enhancement of *j*c centered at *B* || *c* can be seen for all the irradiated samples. In particular, both the trimodal angular configurations show a much broader peak with larger *j*c than that of the parallel CD configuration. It should be noted that there is no drop of *j*c at *B* || *c* for both the trimodal configurations. This result indicates that the three parallel CD families tilted at *θ*i = 0◦ and ±45◦ effectively work as strong PCs in each irradiation direction: flux pinning at *B* || *c* where CDs tilted at *θ*i = ±45◦ slightly contribute to trapping flux lines, is reinforced by CDs along the *c*-axis. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 8 of 22 direction of the splay plane is one of key factors for flux pinning of direction-dispersed CDs, as well as the degree of the direction-dispersion [32,35].

**Figure 7.** Sketch of CDs dispersed in geometry of "another" trimodal-configuration, where a splay plane defined by the three irradiation angles is parallel to the transport current direction. Reprinted with permission from [32], copyright 2016 by IOP. **Figure 7.** Sketch of CDs dispersed in geometry of "another" trimodal-configuration, where a splay plane defined by the three irradiation angles is parallel to the transport current direction. Reprinted with permission from [32], copyright 2016 by IOP.

Interestingly, the behaviour of *j*c around *B* || *c* strongly depends on the direction of the splay plane for the trimodal configuration of CDs: the *j*c of another trimodal-configuration shows a peak at *B* || *c*, whereas standard one exhibits not so much a peak as a plateaushaped curve. In addition, the height of *j*c peak for another tirmodal-configuration is higher than the value of *j*c at *B* || *c* for standard one. For standard trimodal-configuration, sliding motion of flux lines occurs along the tilted CDs at *B* || *c* because of the splay plane parallel to the Lorentz force, resulting in the reduction of the pinning efficiency [33]. The crossed CDs for another trimodal-configuration, by contrast, suppress the motion of flux lines efficiently, since flux lines move across the crossed CDs by the Lorentz force. Thus, the splay plane parallel to the transport current direction provides stronger flux pinning at *B* || *c*, like planar PCs. Furthermore, the *jc* of another trimodal-configuration is the highest even when the magnetic field is tilted from the c-axis. This is probably due to the entanglement of flux lines induced in a mesh of the splay plane tilted from the magnetic field, where the motion of flux lines is suppressed [34]. These results suggest that the direction of the splay plane is one of key factors for flux pinning of direction-dispersed CDs, as well as the degree of the direction-dispersion [32,35].

**Figure 8.** Magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with various CD configurations (Pure: unirradiated samples, Para: parallel CD configuration of *θ*i = 0°, Standard: standard trimodal-configuration, and Another: another trimodal-configuration). Reprinted with permission from [32], copyright 2016 by

*3.2. Modification of Jc Anisotropy by Controlling Number of Heavy-Ion Irradiation Directions*

We further increased the number of the directions of CDs by controlling the irradiation directions (see Figure 9), in order to spread the strong pinning effect of CDs over a wider magnetic field angular range. Figure 10 shows the magnetic field angular depend-

IOP.

IOP.

printed with permission from [32], copyright 2016 by IOP.

**Figure 8.** Magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with various CD configurations (Pure: unirradiated samples, Para: parallel CD configuration of *θ*i = 0°, Standard: standard trimodal-configuration, and Another: another trimodal-configuration). Reprinted with permission from [32], copyright 2016 by **Figure 8.** Magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with various CD configurations (Pure: unirradiated samples, Para: parallel CD configuration of *θ*i = 0◦ , Standard: standard trimodal-configuration, and Another: another trimodal-configuration). Reprinted with permission from [32], copyright 2016 by IOP.

direction of the splay plane is one of key factors for flux pinning of direction-dispersed

**Figure 7.** Sketch of CDs dispersed in geometry of "another" trimodal-configuration, where a splay plane defined by the three irradiation angles is parallel to the transport current direction. Re-

CDs, as well as the degree of the direction-dispersion [32,35].


**Author details**

Bhushan Devidas Meshram1 , Vaibhav Kisanrao Lule1 , Shivani Vyawahare1 and Rekha Rani2 \*

1 Department of Dairy Technology, College of Dairy Technology, Warud, Maharashtra, India

2 Department of Dairy Chemistry, College of Dairy and Food Technology, Agriculture University, Jodhpur, Rajasthan, India

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**4. Message-passing on the chip**

Since the beginning of the multicore era, parallel processing has become prevalent across-the-board. While previously parallel working processors almost exclusively belonged to the domain of datacenters, today nearly every common desktop PC is already a multiprocessor system. And according to Moore's Law, the number of compute cores per system will continue to grow on both the low end and the high end. Already at this stage, there exist multicore architectures with up to twelve entire cores. However, this high degree of parallelism poses an enormous challenge in particular for the software layers.


**Abbreviations**

The following abbreviations are used in this manuscript:

### **Appendix A. Example 1**

To compute the time-response of the multivalued transfer function in (5), we consider the following definition of the inverse Laplace transform:

$$y(t) = \mathcal{X}^{\varepsilon - 1} \left[ \frac{1}{\sqrt{s + k}} \right] = \frac{1}{2i\pi} \int\_{\varepsilon - \infty}^{\varepsilon + \infty} G(s) \varepsilon^{st} ds. \tag{A1}$$

To solve (A1), let the contour *C* be defined as the sum of *Ci*, *i* ∈ [1, 6], as shown in Figure A1. Note that the election of the integration path should be one which avoids branch points, namely, point −*k* in this scenario.

**Figure A1.** Integration path of Example 1.

According to the residue theorem

$$\int\_{\mathbb{C}} G(\mathbf{s}) \boldsymbol{\epsilon}^{\rm st} d\mathbf{s} = 0.\tag{A2}$$

Then, we can express (A1) as

$$\int\_{Br} \mathbf{G}(\mathbf{s}) e^{\mathbf{s}t} d\mathbf{s} = -\sum\_{i=1}^{5} \int\_{C\_{i}} \mathbf{G}(\mathbf{s}) e^{\mathbf{s}t} d\mathbf{s}.\tag{A3}$$

Observe that, for *R* → ∞

$$
\int\_{C\_1} = \int\_{C\_2} = 0,\tag{A4}
$$

and, on the other hand, for *ρ* → 0 we have

$$\int\_{C\_3} = 0.\tag{A5}$$

Thus, it suffices to compute the integration along *C*2 and *C*4 to obtain *y*(*t*). In order to perform such an operation, consider the parameterisation *s* + *k* = <sup>−</sup>*r*, which in polar form can be rewritten as *re*±*iπ*, where the positive sign corresponds to *C*2 and the negative sign corresponds to *C*4. This permits us describe the path *r* ∈ (*k* + *ρ*, ∞), with *δ*, *ρ* → 0, i.e.,

$$\int\_{C\_2 + C\_4} = \int\_{\infty}^{\rho} \frac{e^{-(r+k)t} e^{i\pi}}{\sqrt{r} e^{i\pi/2}} dr + \int\_{\rho}^{\infty} \frac{e^{-(r+k)t} e^{-i\pi}}{\sqrt{r} e^{-i\pi/2}} dr,\tag{A6}$$

since *ρ* → 0

$$\int\_{\mathbb{C}\_2 + \mathbb{C}\_4} = \left(e^{i\pi} + e^{-i\pi}\right) \int\_0^\infty \frac{e^{-(r+k)t}}{\sqrt{r}} dr$$

$$= -2i\sin\left(\pi/2\right) e^{-kt} \int\_0^\infty \frac{e^{-rt}}{\sqrt{r}} dr$$

$$= -2i\sin\left(\pi/2\right) e^{-kt} t^{-1/2} \Gamma(1/2).$$

Now, as we know that

$$
\Gamma(x)\Gamma(1-x) = \frac{\pi}{\sin(\pi x)},
$$

with *x* = 1/2, from (A1) we have,

$$\mathcal{L}^{-1}\left[\frac{1}{\sqrt{s+k}}\right] = \frac{e^{-kt}}{\sqrt{t\pi}}.\tag{A7}$$

This finishes the proof of statement (6).

### **Appendix B. Example 2**

Following the ideas used to find the inverse Laplace Transform of √ 1*s*+*k* shown in Appendix A, we now perform the time-response of (7) (given in Equation (8)) by computing

$$y(t) = \mathcal{L}^{\rho^{-1}} \left[ \frac{1}{\sqrt{s^2 + k}} \right] = \frac{1}{2i\pi} \int\_{c-\infty}^{c+\infty} G(s) e^{st} ds. \tag{A8}$$

Observe that for *k* > 0, we have a complex conjugate branch point, while for *k* < 0 we have two real points. Under these observations, we consider two different integration paths, shown in Figure A2, where Figure A2a and Figure A2b correspond to the case of *k* negative and positive, respectively.

**Figure A2.** Integration path of Example 2. (**a**) *k* < 0. (**b**) *k* > 0.

We first consider the case *k* < 0; thus, we shall consider the path shown in Figure A2a and create a path such that

$$\int\_{C} G(\mathbf{s})e^{\mathbf{s}\mathbf{f}}d\mathbf{s} = 0.$$

Under the assumption that *ρ* → 0,

$$\int\_{\mathcal{C}\_1 + \mathcal{C}\_2} = 0.\tag{A9}$$

Now, *C*3 and *C*4 *s* vary from √*k* − *ρ* to − √*k* + *ρ*, and then we have

$$\int\_{C\_2 + C\_3} \frac{e^{st}}{\sqrt{s^2 - k}} = -\mathbf{i} \int\_{-\sqrt{k} + \rho}^{\sqrt{k} - \rho} \frac{e^{st}}{\sqrt{k - s^2}} + \mathbf{i} \int\_{\sqrt{k} - \rho}^{-\sqrt{k} + \rho} \frac{e^{st}}{\sqrt{k - s^2}} = -2\mathbf{i} \int\_{-\sqrt{k} + \rho}^{\sqrt{k} - \rho} \frac{e^{st}}{\sqrt{k - s^2}}.\tag{A10}$$
  $\text{Since } \rho \to 0,$

*ρ*

$$y(t) = \frac{1}{2\pi\mathbf{i}} \int\_{Br} G(\mathbf{s}) \mathbf{e}^{\mathbf{s}t} d\mathbf{s} = \frac{1}{\pi} \int\_{-\sqrt{k}}^{\sqrt{k}} \frac{\mathbf{e}^{\mathbf{s}t}}{\sqrt{k-s^2}}.\tag{A11}$$

Then, making *s* = *a* cos(*u*), the integral becomes

$$\frac{1}{\pi} \int\_0^\pi e^{kt\cos(u)} du = I\_0(\sqrt{k}t). \tag{A12}$$

We can express the modified first Bessel function in terms of the first Bessel function if − *π* < arg( √*kt*) ≤ *π* 2 : =*e α*

*π*

2 *Iα*( √*kt*)

with *α* = 0:

$$I\_0(\mathfrak{i}\sqrt{k}t) = I\_0(\sqrt{k}t).$$

*Jα*(*i*

√*kt*)

Now, we consider the case where *k* > 0. The inverse Laplace transform of *G*(*s*) can be written in two different forms (see for instance [27]):

$$y(t) = \frac{2}{\pi} \int\_{\sqrt{k}}^{\infty} \sin(st) \frac{1}{\sqrt{s^2 - k}} ds,\tag{A13}$$

$$y(t) = \frac{2}{\pi} \int\_0^{\sqrt{k}} \cos(st) \frac{1}{\sqrt{k - s^2}} ds. \tag{A14}$$

The first Bessel function is given as

$$J\_0(\mathbf{x}) = \frac{1}{\pi} \int\_0^\pi \cos(-\mathbf{x}\sin(\tau))d\tau.$$

Thus, by taking *s* = √*k* sin(*θ*) in (A14), with *θ* ∈ (0, *π* 2) we have

$$y(t) = \frac{2}{\pi} \int\_0^{\frac{\pi}{2}} \cos \left(\sqrt{k}t \sin(\theta)\right) d\theta = \frac{2}{\pi} \frac{\pi}{2} J\_0(\sqrt{k}t). \tag{A15}$$


**7.4.5 Category # 5 – Unclassified data**

The majority of the data were classified in one or other of the categories identified above. However there was a small minority that did not fit any of them. These remained unclassified. Two examples are as follows.

Table 5. Unclassified data.

In light of the foregoing, Table 6 presents the frequency count of the codes generated from the classification of the meaning units.

Table 6. Frequency count of codes emerging from units of meaning.

To the extent that the writing of overviews and the selection and writing of details are two important tasks in the construction of an annotation, the evidence is that these two skills were well represented in the data set. Together they accounted for 69% of the meaning-units coded. However, it should also be noted that they were not used in relation to one another: one did not see the typical pattern of overview followed by supporting details in a given annotation. Instead both were used across different annotations.

In terms of summary writing for an annotation, the issue arises whether all relevant aspects of this skill were accounted for in the data set.

Data MP70 was recognized as a member of this category, in spite of the somewhat tentative nature of the verb. The decision to include it was based on the fact that other attributes of the assertion were evident and the strength of the second part of the verb phrase could be viewed as overshadowing the caution in 'seem'. Data MP108 was also acknowledged as a member of this category, notwithstanding the inclusion of 'the writer' as the apparent source. One wonders whether there was any evidence in the source material to support this

The majority of the data were classified in one or other of the categories identified above. However there was a small minority that did not fit any of them. These remained

MP73 This book excerpt is based upon findings derived from a series of surveys.

MP134 Sun Kyong Lee pointed out that media uses were based on different studies.

In light of the foregoing, Table 6 presents the frequency count of the codes generated from

**Code Number of units of meaning %**

Overview 56 34% Superimposition 12 7% Detail 58 35% Assertion 19 12% Unclassified 18 11%

To the extent that the writing of overviews and the selection and writing of details are two important tasks in the construction of an annotation, the evidence is that these two skills were well represented in the data set. Together they accounted for 69% of the meaning-units coded. However, it should also be noted that they were not used in relation to one another: one did not see the typical pattern of overview followed by supporting details in a given

In terms of summary writing for an annotation, the issue arises whether all relevant aspects

'categorically' stated fact.

Table 5. Unclassified data.

**7.4.5 Category # 5 – Unclassified data**

unclassified. Two examples are as follows.

**Data ID Unclassified meaning units**

the classification of the meaning units.

MP93 He used two papers to scrutinize his research.

Table 6. Frequency count of codes emerging from units of meaning.

annotation. Instead both were used across different annotations.

of this skill were accounted for in the data set.


**4. Results and Discussions**

The experimental results and conditions are summarized in Table 1. In Table 1, *P* is the probability of a flood event; *Q* is the prototype flood event discharge; *t* is the prototype flood event duration; *z* is the prototype grade control datum elevation; *i* is the measured average bed slope (model) upstream of the GCS; *dp* is the maximum general scour depth at the site of 105th Provincial Highway Bridge in terms of *z* = 544 m (i.e., the bed elevation before the Wenchuan Earthquake). In this study, as the detailed hydrograph is not available, the peak flood rate was applied during each flood event. As the flood in this area is caused by intense rain, the flood rising and recession periods are very short and can be neglected. In order to avoid the impacts of local scour and constriction scour on the bed profile, the general scour depth at bridge site was measured upstream of the scour area of the bridge foundation.

**Table 1.** Summary of the experimental conditions and results.

## *4.1. Talweg Profile Upstream of GCS*

Figure 4 shows the talweg profile upstream of the GCS of each GCD *z* for different flood events. Figure 4 indicates that, for each test, the bed elevation immediately upstream of the GCS is approximately equal to the GCS crest (i.e., GCD). For each *z*, the upstream talweg elevation is lower with a lower *P* (higher discharge, *Q*). This is because a higher flowrate has a greater capacity for sediment transport, causing more erosion on the bed. For *z* = 539 m, the bed in −150 m < *x* <0 is flatter with a higher *Q*, as some of the sediment driven by the approach flow is blocked by the GCS, resulting in an aggraded bed near the GCS. For *z* = 533 m and *z* = 527 m, the aggradation in −150 m < *x* < 0 disappears. This is because, for a lower GCD, the sediment above the GCD is flushed downstream over the GCS without any blockage. Figure 4 also indicates that, for a lower *z*, the difference in the talweg profile caused by increasing *Q* is larger. The bed incision due to GCD drop can be affected by two factors: (i) the approach flow capacity for sediment transport; (ii) GCS blockage. The bed is stabilized when these two factors reach a balance. As the GCS only blocks the sediment when the GCD is above the bed, for a lower GCD, factors (i) and (ii) reach the balance at a lower bed level.

**Figure 4.** Upstream talweg profile after different flood events for *z* = 539 m (**a**), *z* = 533 m (**b**) and *z* = 527 m (**c**).

Figure 5 indicates that for each *Q*, the upstream talweg elevation decreases with decreasing *z*. For *P* = 50%, there is an abrupt steepening in the talweg profile for *z* = 533 m and 527 m at *x* ≈ 200 m and *x* ≈ 300 m, respectively. For *P* ≤ 10%, the abrupt steepening in the talweg profile for *z* = 533 m and 527 m disappears. This is because the bed degradation induced by the drop in GCD begins as a head cut erosion process from *x* = 0. For small discharges (*P* ≥ 20%), the sediment transport rate is slow and is unable to fill the head cut erosion area during the flood event. For high discharges (*P* ≤ 10%), the upstream sediment transport rate is high enough to fill the head cut erosion area within the duration of the flood. Figure 5 also indicates that for *P* ≤ 3.3%, the talweg profile of −200 m < *x* <0 is flatter than that of *x* < −200 m for *z* = 527 m. This is because the grade control datum protrudes high enough above the upstream river bed to block the sediment from the upstream, inducing an aggraded bed near the GCS.

**Figure 5.** Upstream talweg profile of each GCDs *z* for *P* = 50% (**a**), *P* = 20% (**b**), *P* = 10% (**c**), *P* = 5% (**d**), *P* = 3.3% (**e**) and *P* = 1% (**f**).

Figure 6 highlights the dependence of the average upstream bed gradient *i* on the flood discharge *Q*. Figure 6 shows that *i* is greater with a lower *z*. As the GCD drop enlarges the elevation difference between *x* = 1300 m and *x* = 0, the bed tends to develop to be steeper. Figure 6 also indicates that *i* is approximately independent of *Q* for *z* = 539 m, but decreases with *Q* for *z* = 533 m and *z* = 527 m. As shown in Figures 4 and 5, the final bed elevation at *x* = 0 is fixed at the GCD. Thus, the increasing *Q* erodes more sediment from the upstream bed, resulting in a lower upstream bed level and a smaller average gradient.

**Figure 6.** Dependence of average talweg gradient *i* on discharge *Q* for different GCDs *z*.

#### *4.2. Transverse Profile Upstream of GCS*

Figure 7 indicates that, for each *z*, the channel cross-section is deeper and wider with a higher *Q*. This is because the increase in *Q* increases the sediment transport capacity of the flow, resulting in greater erosion of the riverbed and riverbanks. Figure 7 also shows that, for a lower *z*, the difference in the cross-section depth and width caused by increasing *Q* is greater. More specifically, as shown in Figure 8, the channel cross-section of each discharge is wider and deeper for a lower *z*. The GCD drop can cause significant bed incision as shown in Figures 4 and 5, inducing mass failures in the riverbank as the incised bed can not support the bank material. Our experimental observations also confirm that, for a lower GCD, more mass failure occurs in the bank.

**Figure 7.** Transverse profile of different flood events (*P* = 1%–50%) at *x* = −800 m for *z* = 539 m (**a**), *z* = 533 m (**b**) and *z* = 527 m (**c**).

**Figure 8.** *Cont*.

**Figure 8.** Transverse profile of different GCDs *z* for *P* = 50% (**a**), *P* = 20% (**b**), *P* = 10% (**c**), *P* = 5% (**d**), *P* = 3.3% (**e**) and *P* = 1% (**f**).

#### *4.3. General Scour Depth at the 105th Provincial Highway Bridge*

Figure 9 highlights the dependence of the maximum general scour depth *dp* at the 105th Provincial Highway Bridge on the discharge *Q* for different GCDs. In Figure 9, for *z* = 539 m, with the help of the GCS, *dp* is approximately independent of *Q*. For a lower *z*, even very small *Q* (*P* = 50%) can cause serious general scour at the bridge site (*dp* ≈ 9.4 m and 14.8 m). For *z* = 527 m, i.e., the GCS is completely removed, the *dp* can reach up to 17.6 m. For the new GCS design plan *z* = 533 m, the minimum *dp* is 9.4 m. Thus, this study suggests building a new GCS with *z* ≥ 539 m or a new bridge with much deeper foundations.

**Figure 9.** Dependence of the maximum general scour depth *dp* at the 105th Provincial Highway Bridge on discharge *Q* for different GCDs *z*.


**Sinan Oncu**

Department of Mechanical Engineering, Bogazici University, Istanbul, Turkey

**Book Series Editor: Efren Gorrostieta Hurtado** Engineering Faculty of the Autonomous University of Queretaro, Mexico


**6. Discussion and implication of CBIS**

Despite all the possible advantages of IS in the context of online businesses today, the research in CBIS has narrowly focused on the cost related aspects. For instance, lack of customer satisfaction and unmet customer expectations are important inhibitors for online business growth. Trust is also another important aspect of CBIS utilization. Possible risks related to the opportunistic behavior of traders are a traditional reason of higher transaction costs in the CBIS environment, and demonstrates the need for CBIS techniques that build trust.

Two major contributions can be derived from this chapter. Firstly, for CBIS researchers, this chapter presents a detailed survey and useful background information on CBIS. Secondly, for CBIS stakeholders, this chapter suggests that for CBIS utilization and customer satisfaction, the three main pillars, i.e. customers, companies and CBIS regulators are needed. This study also categorized CBIS into several categories namely, independent CBIS, buyer oriented CBIS, supplier oriented CBIS, vertical CBIS, horizontal CBIS and the hybrid CBIS. Depending on the specific needs of the companies, they can employ any type of these CBIS. For example, large organizations that have sufficient resources would own say, a vertical CBIS with a multi-tiered system comprising many suppliers. On the other hand, a group of buyers may choose a buyer-oriented CBIS as a platform for finding the best procurement options. However shorter product life cycles and the demand for a larger number of derivatives have driven companies to be adaptive as well as responsive to the volatile environment. This suggests that they may need to consider a hybrid type of CBIS, which provides the benefits of both say the vertical and horizontal CBIS. Research on CBIS categories also ignores important aspects of customer needs and activities that may neutralize many of the hypothesized competitive benefits of fundamental firms. For instance, consumers who need instantaneous satisfaction may be unenthusiastic to rely on CBIS vendors who ship products by courier. Therefore, in this context the hybrid CBIS category involving the use of both virtual and physical presence to attain the needs of purchasers may be a better option.

Without any of the three pillars of CBIS as mentioned earlier, it is unlikely that the CBIS will be sustainable. A CBIS regulator plays a major role in the CBIS industry as they set the rules and regulations in order to control the CBIS applications. In some countries such as Saudi Arabia where there are many regulations relating to culture and religion, CBIS regulators have a huge effect on the sustainability of CBIS. Hence CBIS owners (or operators) need to consider the influence of this pillar. Obviously, the customer as a second pillar of CBIS also plays a very important role for its sustainability, without these pillars the CBIS will not function. Earlier customer focused CBIS research were mainly on the operational, implementation and adoption aspects of CBIS. However, with the introduction of Service Science Management and Engineering (SSME) by IBM, there is a now a focus on value (customer perspective) and value co-creation between stakeholders. Similarly, the company as the third pillar is also equally important. Together these three pillars should work together to co-create value for the stakeholders.


presence of this band allowed us to obtain excellent calibration results with raw spectra data, without any pretreatment (R2 = 0.91). Notably, fat is one of the most important parameters when characterizing donated breast milk as it is the main source of energy for newborns. Furthermore, it provides essential nutrients such as fat-soluble vitamins and polyunsaturated fatty acids [23]. These results showed that the NIR spectra successfully captured quantitative variations in fat, showing the richness of the NIRS spectra.

Similarly, quantitative results could be obtained using the proposed procedure, because NIRS regression coefficients were obtained for energy and total solids, with R2 values higher than 0.9 [5]. Precision values calculated as coefficient of variation (CV% = 100 × SEC/mean calibration set reference values) ranged between 10% and 15% for all the parameters involved in this study. Similar results were obtained in previous research [16] when comparing the results produced by different devices and reference methods. For these parameters, the best results were obtained after applying SNV and the first derivative to the raw spectra. For RP, CP, and CH, not many differences were observed when developing PLS regression with or without pretreated spectra. The R2 value for protein data was higher than 0.75 and for CH, it was higher than 0.8. These values indicated that all the developed models can be used for quantitative analysis.

After studying the calibration statistics of the NIRS multivariate models in depth, the next step was to select the best chemometric models to quantify each macronutrient in breast milk. This choice was made based on the criterion detailed in the Section 2 (the highest r2 value and the lowest SECV) and on the comparison between SEC and SECV, because a gap between SEC and SECV is related to large differences between calibration and prediction results, which indicate that the calibration model was not robust.

Although few differences were found when comparing the NIRS calibration and crossvalidation statistics, the best results for fat (r2 = 0.841, SECV = 0.51), proteins (RP, r2 = 0.512, SECV = 0.21), and carbohydrates (r2 = 0.741, SECV = 1.35) were obtained when no pretreatment was applied to the NIR spectra. For energy (r2 = 0.830, SECV = 9.60), SNV plus the first derivative obtained satisfactory results. As shown in Table 2, the best R2 value for TS was obtained with a first-derivative pretreatment; however, the difference observed between cross-validation and calibration data was too large, indicating that the results were not robust and the validity of that model was limited. For these reasons, we determined that the best model for TS quantification was that without applying any pretreatment to the spectra (r2 = 0.685, SECV = 2.42).

The energy and TS parameters showed the largest differences in SECV and SEC values. The reason for these results may be that both parameters are indirect. This means that they are not directly related to a molecular bond. However, the robustness of the calibrations could be improved by enlarging the sample size and the variability in the breast milk. An update of the calibration models is required when new samples are considered. However, no conclusions could be reached with this calibration and cross-validation data, as an adequate statistic test is needed to quantify the SEP (external validation).

After selecting the best treatments, to confirm the validity of the developed models, we then externally validated the models, predicting all the macronutrients by using the selected models. As detailed in the Section 2, 15 breast milk samples with reference data were selected for external validation and all the parameters were quantified. After quantifying all the breast milk parameters with the developed models, Student's *t*-test was applied to compare the results obtained when analyzing samples using the reference and onsite NIRS method.

As detailed above, the final acceptance or evaluation of the NIRS calibration models necessitated an external validation including samples not involved in the calibration procedure. In this work, 15 breast milk samples were included in the external validation set and quantified with the selected calibration models developed in this study. The selected methods and external validation statistics are detailed in Table 3.

**Table 3.** External validation statistics used for predicting nutritive parameters of breast milk (validation set, N = 15).

SNV: standard normal variate, N1N2N3N4: Savitzky-Golay derivative order, polynomial order of derivative, and left and right intervals for the derivative smoothing, SECV: standard error of cross-validation, SEP: standard error of prediction, RPD = standard deviation of the validation set/SEP; Accuracy %: 100 − ((reference value − predicted value)/reference value) × 100), *t*-critical value for 95% confidence and 14 degrees of freedom = 2.145, RP: raw protein, CP: crude protein, CH: carbohydrates, TS: total solids.

As shown in Table 3, we compared the SEP and SECV values for the selected models. The ratio between SECV and SEP ranged between 0.817 and 1.035 for all parameters except for TS (0.533). The similarity between SECV and SEP confirmed that no difference was found between the external and cross-validation predicted errors, indicating a sufficiently robust calibration for all parameters [24]. For TS quantification, an improvement in the models is required by including new samples and enhancing the multivariate model.

Another statistic that can explain model reliability in NIR spectroscopy is RPD (RPD = standard deviation/SEP). For this parameter, three categories can be defined: (1) excellent models, with RPD > 2; (2) fair models, with 1.4 < RPD < 2; and, (3) unreliable models, with RPD < 1.4 [25]. These values have been applied in NIRS studies; however, no statistical basis has been used to establish these thresholds. Moreover, researchers developed useful calibration models with RPD values lower than the proposed standard values [25]. Considering this statistic in Table 3, we the fat and energy models are categorized as excellent and the RP and HC models as fair. For TS and CP, the range of and variability in the samples should be increased to improve the NIR statistics and obtain a valuable model.

After determining the fit and quality of the calibration models, and taking into account the coefficients of determination and calibration or cross-validation errors, a statistical test including SEPs and reference data was conducted to evaluate the prediction errors of the multivariate NIRS models. In this work, we selected Student's *t*-test to compare paired samples. We applied a paired difference *t*-test to compare the results obtained when samples were analyzed by the reference and NIRS methods. Then, we used the set of differences to build the *t*-statistic using the mean and standard deviation of the differences. Student's *t*-test is a useful statistic strategy for comparing two data sets of quantitative results obtained with different analytical methods. In this study, we compared the reference and predicted data of all samples included in the validation set (N = 15). The results showed that there were no differences when considering a confidence level of 95% because, for all parameters, the calculated *t*student was is lower than 2.145 (theoretical value of *t* for 14 freedom degrees and 95% confidence level). Another parameter that we used to characterize the proposed methodology was accuracy. We calculated the accuracy for all the macronutrients involved in this study, and the best results were obtained for fat and energy with a value of 94%.

We could find no information about analytical methodologies for onsite and real-time quantification of the macronutrients in breast milk. Table 4 summarizes the most relevant studies conducted using NIRS technology, including the instrumentation employed to quantify macronutrients (high-performance laboratory instruments). Only dos Santos et al. [14] used a portable NIRS instrument to classify breast milk in colostrum, transition milk, and mature milk, which are the three stages of the lactation period.

**Table 4.** An overview on reported NIRS-based methods for breast milk analysis.

Lab: laboratory instrument; N = number of samples involved in the study.

Focusing on spectroscopic laboratory methodologies, previous researchers evaluated and compared the use of near- and mid-infrared instruments vs. reference methodologies using high-performance laboratory devices [28]. More specifically, the macronutrients quantified were fat, protein, and carbohydrates. The NIRS instruments employed were precalibrated NIRS laboratory devices, scanning in a range of 1200–2400 nm. No information about the statistics of calibration models were included in this work; however, external validation statistics can be compared with our results. The values of coefficients of determination detailed by Fusch et al. for validation were 0.76 for protein, 0.01 for lactose, and 0.79 for fat. In our study, employing a portable device and developing our own calibration models, the coefficient of determination of cross-validation was 0.52 for protein, 0.74 for HC, and 0.84 for fat MISSING [28].

Table 5 compares the external validation statistics obtained with laboratory instrument vs. the developed portable-device methodology by computing the linear regression of the reference and predicted NIRS data [28]. To evaluate the random error in the prediction based on regression results, the Sy/x statistic (random error in the y-direction, y-direction indicates the prediction values and x-direction reference values) was calculated. Comparing these data with SEP values (Table 3) for fat, RP, and HC, we observed that the regression error (Sy/x) was equal or lower than the error obtained in external validation (SEP), confirming the validity of the developed models.

**Table 5.** Comparison of external validation statistics: Ref. [28] (laboratory instrument) vs. the proposed methodology (portable device).

RP: raw protein, CH: carbohydrates, r2: coefficient of determination, Sy/x: random errors in the y-direction, y: prediction values, x: reference values.

Another NIRS strategy for macronutrients milk analysis was carried out by de la Roza et al. [2], who developed in-house NIR calibrations with a high-performance laboratory instrument (working range 400–2500 nm) for fat, protein, and nonfat total solids in cow milk. The best result, with an R2 value of 0.971, was obtained for the quantification of fat, applying mathematical SNV, detrend, and second derivative pretreatments. The R2 value is similar to that obtained in this work (0.910). However, for total solids, the values of the calibration coefficient of determination for cross-validation were lower than 0.700 (r2 = 0.612) [2], and better results, above 0.750, were obtained using our handheld portable instrument (r2 = 0.787).

#### **4. Conclusions**

In this work we focused on the development of a real-time and simple methodology to quantify the macronutrients in breast milk. Notably, the implementation of this procedure requires the use of low-cost and handheld NIRS instruments. Moreover, expert personnel are not required for analyzing samples, facilitating the quality control procedure in the feeding of newborns in neonatology units.

In this paper, we demonstrated the feasibility of using a cheap and easy-to-use handheld NIRS instrument with a narrow scanning range, from 1596 to 2396 nm, and a small scanning window to control the quality of breast milk. By using a multivariate strategy and different pretreatments, we developed quantitative calibration models to determine the energy, fat, carbohydrate, and protein contents in this type of sample, with coefficients of determination for calibration (R2) higher than 0.79 for all parameters. These results, obtained with a limited number of breast milk samples (68 samples), can be considered as a first step in the development of an appropriate method, even if more work needs to be carried out to improve the equations and to include more samples in the database. The interpretation of the results obtained for fat analysis demonstrated the richness of NIRS spectra because the presence of specific bands shows excellent potential for constructing useful quantitative models.

Prior to implementation, external validation was required. We tested the proposed methodology with breast milk samples not involved in the calibration procedure, and nonsignificant differences were observed when comparing the reference and portable NIRS methods. The accuracy obtained for the tested parameters was higher than 90%. Our results suggest that NIR sensor measurements of macronutrients are acceptable for clinical use in breast milk banks. The limitation of the proposed method is related to the range of values for each nutrient; however, further improvements can be achieved by including new samples to update this first calibration method.

**Author Contributions:** Conceptualization, F.F., J.M.C.-F., M.L.F.-S., A.S., and B.F.-C.; methodology, A.S., C.M., and S.F.; validation, C.M., S.F., A.S., and B.F.-C.; formal analysis, J.M.C.-F. and M.L.F.-S.; investigation, A.S. and C.M.; resources, A.L., F.F., J.M.C.-F., M.L.F.-S., and A.S.; data curation, S.F. and C.M. writing—original draft preparation, C.M.; writing—review and editing, A.L., F.F., J.M.C.-F., M.L.F.-S., A.S., and B.F.-C.; visualization, A.L. and F.F.; supervision, A.S.; funding acquisition, A.L., F.F., J.M.C.-F., and A.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Spanish Ministry of Science and Innovation (PID2020- 117282RB-I00 and MCI-20-PID2019-109698GB-I00), by the Principado de Asturias GRUPIN IDI/2021/ 000081, and by "Fondo de investigación en Salud" (FIS) from the Instituto de Salud Carlos III in Spain (Project PI16/02084) co-financed by the Feder Programme of the European Union.

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki, and approved by the Ethics Committee of Hospital Central de Asturias (Proyecto n◦ 72/16; 05 May 2016).

**Informed Consent Statement:** Each mother provided written informed consent for donating the samples for this study, which was approved by the institutional review board.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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*2.6. Characterization of Assembled DOCs Micellar Structures by AFM*

Atomic force microscopy was performed using a MultiMode 8™ scanning probe microscope (Bruker, Santa Barbara, CA, USA) connected to a NanoScope® V controller (Veeco, Plainview, NY, USA). The images were obtained using tapping mode in air with NSG10\_DLC cantilevers (typical curvature radius 1 nm, resonant frequency 255 kHz, force constant 11.5 N/m) from NT-MDT Spectrum Instruments (Zelenograd, Moscow, Russia). Oligonucleotides containing dodecyl groups were diluted to 1.5 μM in TAM buffer. The reactions were equilibrated for 3 h at 25 ◦C before 6 μL of this solution was deposited onto a freshly cleaved mica surface (7 × 7 mm, NT-MDT Spectrum Instruments, Zelenograd, Moscow, Russia) and allowed to adsorb for 5 min. The surface was then washed thrice with 200 μL of 18 MΩ grade water and dried by strong argon flow. Samples were dried for 10 min prior to imaging.


*Article* **KeyNet: An Asymmetric Key-Style Framework for Watermarking Deep Learning Models**

**Najeeb Moharram Jebreel \*, Josep Domingo-Ferrer, David Sánchez and Alberto Blanco-Justicia**

CYBERCAT-Center for Cybersecurity Research of Catalonia, UNESCO Chair in Data Privacy, Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Catalonia, Spain<EMAIL_ADDRESS>(J.D.-F<EMAIL_ADDRESS>(D.S<EMAIL_ADDRESS>(A.B.-J.) **\*** Correspondence<EMAIL_ADDRESS>Tel.: +34-977558270

**Abstract:** Many organizations devote significant resources to building high-fidelity deep learning (DL) models. Therefore, they have a great interest in making sure the models they have trained are not appropriated by others. Embedding watermarks (WMs) in DL models is a useful means to protect the intellectual property (IP) of their owners. In this paper, we propose *KeyNet*, a novel watermarking framework that satisfies the main requirements for an effective and robust watermarking. In *KeyNet*, any sample in a WM carrier set can take more than one label based on where the owner signs it. The signature is the hashed value of the owner's information and her model. We leverage multitask learning (MTL) to learn the original classification task and the watermarking task together. Another model (called the private model) is added to the original one, so that it acts as a private key. The two models are trained together to embed the WM while preserving the accuracy of the original task. To extract a WM from a marked model, we pass the predictions of the marked model on a signed sample to the private model. Then, the private model can provide the position of the signature. We perform an extensive evaluation of *KeyNet*'s performance on the CIFAR10 and FMNIST5 data sets and prove its effectiveness and robustness. Empirical results show that *KeyNet* preserves the utility of the original task and embeds a robust WM.

**Keywords:** deep learning models; ownership; intellectual property; watermarking; security and privacy; private model