**5. Conclusions**

This case study presents a two-step workflow using thresholds to discriminate wet snow and firn for SAR data. In a first step, the workflow distinguishes dry and wet surfaces and subsequently analyzes wet surfaces for wet snow and firn with a second threshold value. Deviations to the extent of snow covered areas derived from visual and shortwave infrared channels are less than 10% (8.5%) in area for C-band data. WSCAF is sensitive to increases in threshold values, which can lead to offsets up to 18.1%. Average offsets of annual minimum in WSCAF from SAR data and field data on annual AAR are at below 10% (8.2%) as well for three observed GYs and three different glacier areas. For analysis, we included 12 individual glaciers covering a wide range of elevation and exposition as well as area extent. All glaciers are located within the Rofental, Austria. For two glaciers within this study, long-term mass balance series are available. We used these time series to establish linear relationships between AAR and B and compared field measurements on B with outcomes for the relationships for SAR derived AAR values. Deviations between field assessments of B and SAR derived values are at 200–300 mm w.e. on average. Such results are not an improvement compared with conventional measurements but enable mass balance estimates for regions not accessible or too dangerous for conventional mass balance observations. Results are very encouraging and demonstrate the feasibility of the proposed workflow to derive AAR from SAR data. In addition, we could show that glacier surface conditions during the melt season can be quasi-continuously be monitored using S1 SAR data, which is essential for glacier runoff modeling. Implementation of this workflow for other regions worldwide has to be analyzed with extended SAR data acquisitions. However, apart from SAR data, solely the availability of DEMs with sufficient accuracy is required to apply the proposed workflow.

**Author Contributions:** A.H. performed the scientific analysis, acquired the optical data, designed the structure and prepared the manuscript. A.W. is responsible for the download of SAR data and geocoding in the Kennaugh processing chain. A.S. provided the Kennaugh processing chain. C.M. contributed with the design and planning of the study and helped to improve the quality of the manuscript. All authors contributed to editing the manuscript.

**Funding:** This research received funding by the German Science Foundation through DFG grant HE7501/1.

**Acknowledgments:** We would like to thank the Copernicus Service for providing the Sentinel-1 and Sentinel-2 data free of charge and sincerely appreciate the support by Rainer Prinz, Irmgard Juen and the Institute of Atmospheric and Cryospheric Sciences at University Innsbruck, Austria for providing data and information about HEF and KWF. Landsat data were obtained through GLOVIS USGS. A.H. was supported by DFG grant HE7501/1.

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


*3.2. Tactical Path Planning*

Tactical planner is aimed at fast finding a path that can be followed by the UAV if safety and effectiveness of the strategic path are jeopardized during the flight. Optimality is non-accounted for at this level, and the first feasible alternative is considered as tactical solution. Therefore, all the information sources, which are only used for the aim of cost definition (i.e., landing site location and ground risk) are discarded at tactical level, and their modification cannot trigger any level of tactical replanning. Conversely, updates of GNSS maps, fixed and mobile obstacles and wind conditions may call for trajectory update. As far as wind modification is concerned, it not only alters the UAV energy consumption, but it also modifies the zones in which the UAV is allowed to fly due to the maximum admissible wind velocity. Tactical path planner assumes the ownship has a lower priority than the other UAVs, so it has to maneuver in case of conflict. It implements three different solutions, referred to as levels in Figure 3, that are specifically designed to counteract several events that could occur during the tactical phase. The three levels are characterized by an increasing level of computational complexity and their performance is summarized below. For further algorithmic details, the reader is referred to [16].

of the trajectory because it is informed to return to the strategic path. The global nature of this approach avoids sequential replanning if multiple unfavorable events are experienced by the UAV, thus saving time. Due to the spatial modification of the trajectory, this solution is not only able to deal with both fixed and mobile obstacle geometries, but it can also be used to counteract wind velocity and GNSS coverage maps alteration. The heuristic nature of the RRT makes this solution non-deterministic. In addition, a higher computational time is experienced with respect to the previous approach. However, since only a local modification is provided to the strategic path, its optimality remains almost unaltered while also providing a small increase in flight time, as demonstrated in [16].

3. *Level 3* of the tactical planning provides a global modification of the trajectory starting from its last non-corrupted point. From that point, a completely new trajectory is recomputed with an algorithm still based on RRT, but not informed to return to the strategic trajectory. This solution, which completely alters the path after the unfavorable event, should be chosen when a significant modification of the flight conditions has been experienced with respect to the scenario available at the strategic level. Due to the similar algorithmic scheme, this level shares the same heuristic nature of *Level 2*, as well as the higher computational time with respect to *Level 1*.

Among the proposed solutions, the one to be chosen during tactical phase is not trivial to be identified. Although a simple geometry consideration can be made to deem whether to use *Level 1* solution or not, this is not true for the other two levels and their output must be compared to this aim. Therefore, the tactical planner is conceived to run all the levels sequentially and compare their solutions, if available, to choose the one with the minimum cost. A flowchart of the tactical planning is reported in Figure 4.

**Figure 4.** Tactical path planner flowchart.

*Level 1*, which has the lowest computational cost, is the first to be run (it runs only if compliant to the conflict geometries), then *Level 2* is queried. The level sequence runs until a timeout, and the tactical output is picked among all the available solutions at that time. During the flight, the current path is checked for any unfavorable event (i.e., contingency). If the time to the contingency (*tcoll*) is greater than the replanning timeout (*trep*), the tactical replanning levels are run sequentially and the best cost path is selected to update the flight plan. In the case no available solution is found by tactical planning or *tcoll* ≤ *trep*, contingency landing actions are activated.

#### **4. Use Cases**

Strategic and tactical pipeline have been applied to two test case scenarios. The first represents an urban air taxi problem, specifically designed to transport passengers from airport to business center and port. The second scenario includes the delivery of medical supplies from the mainland to an island, thereby saving time with respect to ship-based transportation. Two scenarios have been identified in the Naples area and its surroundings and are reported in Figure 5. Risk, landing site, wind and GNSS coverage maps estimated with three different thresholds, i.e., *D*1 = 2, *D*2 = 3, *D*3 = 4 are reported both for air taxi and medical delivery cases in Figures 6 and 7, respectively.

**Figure 5.** Test case scenarios. (**a**) Air taxi scenario. Top, lateral view and satellite map. (**b**) Medical delivery scenario. Top, lateral view and satellite map.

**Figure 6.** Air taxi scenario. (**a**) Risk and (**b**) landing site intensity maps. (**c**) Top view of wind direction, identified by blue vectors. GNSS coverage maps associated to (**d**) *D*1 = 2, (**e**) *D2* = 3 and (**f**) *D*3 = 4.

Because the two identified scenarios have a huge extension, the GNSS coverage map has been computed only in a portion of the environment which is closer to the start or the end point of the trajectory. They were obtained using a starting time of 11:30 UTC of 19th April 2022. A time interval of 20 min has been considered, with a time span of 5 min. The ground grid has 5 m spacing. A uniform wind intensity of 5 m/s has been used for both missions.

The air taxi scenario is reported in Figure 5a. It envisages transfers from Capodichino airport to Naples business center or port. The three locations have been represented on the map with an asterisk, a cross and a circle, respectively. Both the top and lateral views have been reported in the Earth north up (ENU) coordinate frame originated at 40◦51 56 N, 14◦17 20 E, as well as the rectangles where GNSS coverage maps have been computed. For the sake of concreteness, the satellite map of the identified area is also reported. The lateral view highlights the high slope of the scenario. A maximum flight altitude estimated above the ground level and equal to 150 m has been assumed. Two missions have been considered, i.e.:

The medical delivery scenario involves the Procida island and its closest city on the mainland, i.e., Monte di Procida, which is about 4 km far. Even if several ship connections, taking about 16 min, are organized in the summer season (from June to September), very few transportations (twice a day and only on weekdays) are foreseen in the winter season, making impossible to directly deliver urgent medicines. A dedicated drone service could not only spare time but also be operated on-demand. The scenario extension (both in the lateral and top view) and its satellite view have been reported in Figure 5b. The start and arrival location includes a pharmacy in Monte di Procida (40◦47 20 N 14◦3 0 E and 100 m altitude) and the Procida local medical unit (40◦45 25 N 14◦1 11 E and 60 m altitude), which are reported with a cross and a circle in the figure, respectively. A maximum flying altitude of 150 m above the terrain level (or the sea level when the aircraft flies in the Procida channel) has been assumed.

#### **5. Results**

Strategic and tactical planning have been carried out assuming as aircraft a DJI M300 RTK [27], whose main parameters are reported in Table 1. Navigation performance of the IMU sensor has also been included, which is assumed to be the one of the medium grade IMU HG1120CA50 from Honeywell [28]. The positioning error threshold is assumed to be equal to 2 m so that any trajectory which overcomes this value at least once during the flight must be discarded. In order to trigger every tactical level to output a solution, in this work, tactical information is only limited to intruder trajectory updates. The entire path planning pipeline results will be detailed in the medical delivery scenario, which involves a single mission, in Section 5.1. On the other hand, results related to the air taxi scenario are shown in Section 5.2.

**Table 1.** Vehicle specifics.

1 Only accelerometer parameters are included since navigation error covariance propagation is run with a simplified approach.


*2.3. Universal Solution for Arbitrary Pressure Gradient*

The analysis of a number of scientific papers for the purposes of this review revealed that there is a universal solution that can be used to determine the velocity profile for any change in the pressure gradient. Information about this solution will be the topic of this subsection.

Fan in his Ph.D. thesis [61] derived analytical solutions for: (a) impulsive pressure gradient (here the pressure gradient is a function of Dirac delta function); (b) flow under a constant pressure gradient (analogous to RGS solution); (c) flow under a harmonically oscillating pressure gradient; (d) a general solution by superposition integrals and (e) a general solution by the transformation of the governing equation of motion to a homogeneous equation. The latter helped Fan to derive a final analytical solution for an accelerated flow in a pipe with a rectangular cross-section, which will not be discussed due to limited practical applications. The most important solution according to this subsection title is the general solution defined by superposition integral. Since the considered problem is linear, Fan noticed that the solution for any arbitrary *f*(*t*) can be obtained by one of the following superposition integrals:

$$v(r,t) = -\int\_0^t f(u)\overline{v}\_1(r,t-u)du = -\int\_0^t f(t-u)\overline{v}\_1(r,u)du,\tag{18}$$

where: 1 *ρ ∂p ∂x* = *f*(*t*) and *v*1 *r*ˆ, ˆ*t* = 2 ∑∞ *n*=1 *J*0(*r*ˆ*λn*) *λn J*1(*λn*)*e*−*λ*2 *n* ˆ*t* is the solution that Fan obtained for impulsive pressure gradient, or:

$$v(r,t) = -f(0)\overline{v}\_2(r,t) - \int\_0^t f'^{(u)}\overline{v}\_2(r,t-u)du = -\int\_0^t f(u)\frac{\partial \overline{v}\_2(r,t-u)}{\partial t}du,\tag{19}$$

where *v*2(*r*, *t*) is the RGS solution *v*2(*r*, *t*) = 1 4*ν R*2 − *r*2 − 8*R*2 ∑∞ *n*=1 *J*0(*λn r R* ) *λ*3 *n*·*J*1(*λn*) *e* −*λ*2 *n ν R*2 *t* .

The First Fan integral solution Equation (18) is of simple mathematical structure. The second solution (known as Duhamel's integrals) is based on the more demanding RGS solution Equation (19). Both superposition solutions described by Equations (18) and (19) were derived for the case with the initial flow at rest (mean velocity equal to zero). A solution that takes into account the initial flow was derived by Daneshyar [62]. Daneshyar gives a solution for an arbitrary *f*(*t*), using the theory of integral transforms to solve the main Equation (1). He proved after Sneddon [63] that if *ξn* is chosen to be a root of:

$$J\_0(R\xi\_n^x) = 0\tag{20}$$

then

$$\int\_0^R r \left( \frac{\partial^2 v}{\partial r^2} + \frac{1}{r} \frac{\partial v}{\partial r} \right) l\_0(r \xi\_n) dr = -\xi\_n^2 \overline{v} \tag{21}$$

where

$$
\overline{v} = \int\_0^R r v(r, t) J\_0(r \xi\_n) dr \tag{22}
$$

is the finite Hankel transform of *v*. When both sides of Equation (1) are multiplied by *r J*0(*rξn*) and integrated (within the limits 0 to *R*), the following ordinary differential equation is obtained for *v*:

$$\frac{d\overline{\upsilon}}{dt} + \nu \mathfrak{J}\_n^2 \overline{\upsilon} = f(t) \int\_0^R r \mathfrak{J}\_0(r \mathfrak{J}\_n) dr = f(t) \frac{R}{\mathfrak{J}\_n} \mathfrak{J}\_1(R \mathfrak{J}\_n) \tag{23}$$

The solution that satisfies the initial condition *v*(*ξn*, 0) = *v*0 is:

$$\overline{\sigma} = \int\_0^t f(u) \frac{R}{\tilde{\xi}\_n} f\_1(R\tilde{\xi}\_n) \exp\left[-\nu \tilde{\xi}\_n^2 (t-u)\right] du + \overline{\sigma}\_0 \tag{24}$$

And, next, with the inversion theorem of finite Hankel transforms, a general solution is found to be:

$$\nabla v = v\_0 + \frac{2}{R^2} \sum\_{n=1}^{\infty} \frac{J\_0(r\_{5,n}^{\pi})}{\left[f\_1(R\_{5,n}^{\pi})\right]^2} \overline{v} = v\_0 + \frac{2}{R} \sum\_{n=1}^{\infty} \frac{J\_0(r\_{5,n}^{\pi})}{\overline{\xi}\_n I\_1(R\_{5,n}^{\pi})} \int\_0^t f(u) \exp\left[-\nu \overline{\xi}\_n^2 (t-u)\right] du \tag{25}$$

that is valid for an arbitrary pressure gradient (hidden under *f*(*t*) function).

It can be now noticed that substituting for *Rξn* = *λn* one gets *ξn* = *λn*/*R*, which, when inserted into the above formula, will reduce this solution to the following form:

$$v = v\_0 + 2\sum\_{n=1}^{\infty} \frac{l\_0\left(\frac{r}{R}\lambda\_n\right)}{\lambda\_n f\_1(\lambda\_n)} \int\_0^t f(u)e^{-\lambda\_n^2(t-u)} du,\tag{26}$$

In the special case of the above solution, *v*0 can be treated as an initiation laminar flow profile of steady Hagen–Poiseuille type flow.

A careful literature review reveals that universal solutions of this type were derived many times. Chronologically, the earliest form of this solution was presented by Vogepohl in a short note published in 1933 [30]. Then in 1956, Roller, in his master's thesis [64], noticed (similarly to Daneshyar about 15 years later) that the solution of the Navier momentum equation can be obtained with the use of the analogy to the temperature distribution in a cylindrical rod (defining the analogous boundary and initial condition) [63]. Zielke in his Ph.D. thesis [65] rederived Fan's solution in the form of Equation (19) using Laplace transforms. Hersey and Song by using Laplace transforms [66], and Avula with the help of the Cauchy residue and convolution integral theorem [53], derived the same solution but based on different normalized quantities. These solutions were again derived and used with the help of the eigenfunction method in the work of Xiu et al. [67], where the starting flow was analyzed, and in the Sun and Wang paper [68], where the water hammer case (starting from steady Hagen–Poiseuille flow) was examined:

$$\psi(\mathbf{\hat{r}},\mathbf{\hat{x}},\mathbf{\hat{t}}) = \sum\_{n=1}^{\infty} \frac{16f\_0(\mathbf{\hat{r}}\lambda\_n)}{\lambda\_n^3 f\_1(\lambda\_n)} e^{-\lambda\_n^2 \mathbf{\hat{r}}} + \sum\_{n=1}^{\infty} \int\_0^{\frac{\pi}{2}} \frac{2f\_0(\mathbf{\hat{r}}\lambda\_n)}{\lambda\_n f\_1(\lambda\_n)} \left[ -\frac{\partial \hat{H}(\mathbf{\hat{x}},\mathbf{u})}{\partial \mathbf{\hat{x}}} \right] e^{-\lambda\_n^2 (\mathbf{\hat{t}} - \mathbf{u})} d\mathbf{u} \tag{27}$$

where: *x*ˆ = *x*/*L*; *r*ˆ = *r*/*R*; *v*ˆ = *v*/*v*0 and *H*ˆ = Δ*pR*2 *Lμv*0 .

In the above equation, an interesting identity is used (for initial time ˆ*t* = 0), that can be found in many papers among them the ones discussed in this review i.e., Szyma ´nski [13], Gerbes [17], Xiu et al. [67], etc:

$$\sum\_{n=1}^{\infty} \frac{8f\_0(\lambda\_n \mathfrak{f})}{\lambda\_n^3 f\_1(\lambda\_n)} = (1 - \mathfrak{f}) \text{ for } 0 \le \mathfrak{f} \le 1 \tag{28}$$

The most recent study in which this universal equation was re-derived and examined is Lee's paper published in 2017 in Applied Mathematical Modelling [69]. The motivation of this section is to systematize the derivation of the universal formula discussed above. The list of references is presented in Table 1.

**Table 1.** A list of works in which a universal formula was derived.

## *2.4. Comments on the Pressure Gradient Driven Flows*

As noticed, the formulas discussed above concerned pipes with circular cross-sections. Readers interested in other solutions, e.g., similar accelerated flow in ducts with different geometry, are referred to other works: the solution to this problem for ducts with a rectangular cross-section was derived in the works of Fan and Erdogan [21,61,72]; start-up flow in an annulus was developed by Müller [73]; for other cross-sections, an intensive study was carried out by Laura [22]; solution for pipes, taking into account the slip of the fluid on the wall [74]; start-up flow in a circular porous pipe [75]; development of unsteady flow at the entrance length of a circular tube starting from rest [19,20,54,76]; the effects of time-dependent viscosity [77–79]; unsteady laminar flow in tubes with a tapered wall thickness [80], etc.

Due to the need to use the zeros of the Bessel function, the presented solutions are a challenge, because it is usually necessary to write a short program in software such as Matlab or Wolfram Mathematica, hence the approximation forms of these formulas discussed by Muzychka-Yovanovich [23,24] and Urbanowicz et al. [4] are also an interesting proposition. It is also worth adding that governing equations of motion, are respectively analogous to heat conduction in a long cylinder with constant thermal conductivity [81]. So all the results presented in this paper for laminar flows are directly transformable to the solution of heat conduction in long cylinders with internal heat generation (simply replacing pressure gradient *G* by heat generation source term . *g cP*·*ρ* ; kinematic viscosity *ν* by thermal diffusivity *α* and velocity field *v*(*r*, *t*) by temperature field *T*(*r*, *t*)).

Moss developed [82] a dimensionless flow acceleration parameter that takes a zero value in the case of an impulsively begun flow and non-zero values for exponentially increasing flows. When this parameter is increased beyond a critical value (7.059), the boundary layer never merges. The method developed by Moss is suitable for the application of any stability analyses of unsteady flows, which is very useful to study the physical insights of different flow fields. Pozzi and Tognaccini [83] have extended the analysis of the present accelerating problem in pipes for the thermo-fluid dynamic field arising in an infinite pipe with a circular section when the incompressible fluid is impulsively started from rest by a sudden jump to a constant value of the axial pressure gradient. These authors derived analytical solutions for the temperature field taking additionally into account the dissipation of kinetic energy (Eckert number different from zero) in the relevant case of Prandtl number equal to one. The final solution has been obtained and discussed for four cases depending on the condition imposed on the wall: constant temperature, adiabatic wall, assigned heat loss, and assigned constant flux.

To sum up, the analysis of the presented analytical solutions of accelerated flows in pressure lines forced by a change in pressure gradient shows that:


**2. Synthesis/biogenesis of miRNA**

Synthesis of miRNA takes place in the nucleus as well as in the cytoplasm. Genes encoding miRNAs are present in the form of a cluster and contain introns (**Figure 1**). These genes are transcribed by polymerase II with the generation of the primary precursor pri-miRNA. This precursor miRNA consists of a 30 poly-A tail and a 50 end cap [19, 20] with a stem-loop structure. RNase 3 Drosha cleaves this structure with the help of its Pasha cofactor DGCR8. This resultant cleaved, precursor structure is known as pre-miRNA and consists of �70–90 nucleotides [21]. This �70 nt precursor is exported to the cytoplasm by Exportin-5.

In the cytoplasm, the whole pri-miRNA is recruited by a RNA-induced silencing complex (RISC) and is converted into mature miRNA. These are mediated by an RISC leaching complex (RLS), which is basically a multiprotein complex and consists of a double-stranded RNA domain protein (DICER), tar RNA-binding protein (TARB), and the Ago 2 protein. The RNAse 3 DICER along with its cofactor yields duplex miRNA (19–25 nucleotide duplex miRNA with 2 nucleotide overhangs at each 30 end). During the process of cleavage, two strands are formed, namely, a functional and a passenger strand. The functional strand along with the Ago protein (RISC) is involved in gene silencing function, while the passenger strand is degraded due to its instability. This miRISC incorporates one strand of miRNA (functional strand and guide strand) so that it takes the guidance from this complex to target mRNA (complementary) for its degradation or inhibition at the translational level [22]. miRNA is processed in the cytosol and transported to the blood. It is resistant to degradation because it is carried by complexes of lipoprotein inclusions [23] or in the form of exosomes [24, 25].

**4. Diagnosis of cancer**

**Figure 2.**

**Figure 3.**

*Mechanism of miRNA.*

*Mechanism of action of miRNA.*

*MicroRNA: A Signature for Cancer Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.90063*

**5.1 Breast cancer**

**5**

There are reported differences in the expression pattern of miRNA in normal

downregulated in different kinds of cancers [28]. Due to its small size and resistance to RNase-mediated degradation, they have the potential as powerful biomarkers for cancer diagnosis [29]. miRNA expression is involved with the rearrangement of chromosomes, methylation of the promoter region, and transcriptional regulation. miRNA-mediated aberrations in one or more of these processes can culminate in

and cancer cells [27]. Some miRNAs are overexpressed, while the others are

alterations in protein and mRNA expression [30].

**5. Types of miRNA and cancer according to organs**

Different miRNAs are involved in different types of cancers:

Breast cancer is the most prevalent form of cancer in women. Among 12.7 million cancer cases globally, breast cancer is most frequently diagnosed, that is, 23 and 14% deaths due to breast cancer have been reported [1, 31]. The alarmingly increasing mortality data coupled with increases in relapses warrants an improved molecular understanding of the etiology and mechanistic details that contribute to the chemoresistance.  These are ErbB2+ (epidermal growth factor receptor 2-positive (also called HER2)), luminal A

**Figure 1.** *Biogenesis of microRNA.*